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R-7824-5489
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VALIDATION OF
PULSE TECHNIQUES FOR
THE SIMULATION OF
EARTHQUAKE MOTIONS
IN CIVIL STRUCTURES
May 1983
Prepared Under
Any opinions, findings, conclusions or rEX:ommendations expressed in this publication 3,e those of the author(s) and do not necessarily reflect the view~ of the National Science Foundation.
National Science Foundation Grant No. CEE77-150 1 0
REPRODUCED BY NATIONAL TECHNICAL INFORMATION SERVICE
u.s. DEPARTMENT OF COMMERCE SPRINGFIELD, VA. 22161
AGBABIAN ASSOCIATES 250 North Nash Street P.O. Box 956 El Segundo, CA 90245-0956
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PAGE J NSF /CEE-83211 . . - !
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L "port Cat. May 1983 !
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Validation of Pulse Techniques for the Simulation of Earthquake Motions in Civil Structures • ______________________ i
7. Aut1'IoI'{.) a. ~rrormj"4 .9~"iz.tlon ~.~. No. '
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Agbabian Associates 250 North Nash Street P:O. Box 956 El Segundo, CA 90245-0956
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Directorate for Engineering (ENG) I National Science Foundation i 1800 G Street, N. W . t-1-4·-------------------:
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'I----------------,--~--------.--.--.-----______ I lL;::~~~:I1:a;e_;;~sented of research undertaken to validate the application of pulse Ii
techniques for the simulation of earthquake motions in civil structures. A pulse train algorithm was developed and is shown to closely approximate structural motions induced by earthquakes. A simple anti-earthquake algorithm was also developed. This algorithm, when used in conjunction with various types of pulse units, shows promise in the reduction of'structw"al motions at the damage or ~ife-threatening thresholds. The anti-earthquake algorithm is presently limited to preselected fixed ampl itude pulses. Two gas pulse generating systems were produced end are said to be in a state of operational readiness. It is suggested that additional calibration tests at low to medium nozzle throat settings be conducted. In addition, surge suppressors should be added to the plenum chembers to improve nozzle efficiencies and to reduce the interaction of pneumatic surges with the plenum chamber balancing piston,
17. ~mem ANoI~. D. ~r!~ors
Earthquakes Algorithms Structures
b. J.dontir .. ~/~-~ Tarms
Pulse techniques Ground motion
Dynamic structural analysis Generators Earthquake resistant structures
F.B. Safford, jPI S.F. ~lasri, jPI
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R-7824-5489
ABSTRACT
This research project was undertaken to validate the appli
cation of pulse techniques for t.."lJ.e simulation of earthquake
motions in civil structures. Major efforts were in the develop
ment of algorithms to generate pulse t~ains and to develop
digitally programmable gas pulse thrusters.
An algorithm employing adaptive random search was success
fully developed to generate pulse trains which, when applied to
a system, will closely approximate structural motions induced by
earthquakes. This algorithm permits placement of pulse excita
tion units in multiple locations of test convenience. Computer
studies of several structures yielded information on the per
formance required for pulse units with respect to optimum
exciter locations, phase effects, thrust magnitude, pulse
widths, and impUlse. A rudimentary anti-earthquake algori t.'ml
was also developed which has potential applications at extreme
structural motions to reduce severe building damage or life
threatening situations.
~NO programmable cold gas pulse systems were successfully
developed and are available for tests. The gas pulse systems
performed reliably and safely. Start-up, shut-down and repeat
tests may be performed quickly and efficiently. Changing pulse
train commands involves entering only time and amplitudes on the
keyboard of the control microcomputer. The system is readily
transported to test sites and set-up time is expected to be less
than a day. Peak output force is slightly less than 10,000 Ibf
and minimum pulse width is about 25 ms. Signal monitors provide
time history records of input command signals, metering nozzle
position, chamber pressure and output force.
Demonstration tests on a single story commercial structure
were conducted and the gas Dulsers performed as intended.
Output forces and pulse durations obtainable wi t..~' these units
make them suitable for use on small buildings, large equipment,
plplng systems, open frame structures and electric power distri
bution centers.
Preceding page blank III
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ACKNOWLEDGEMENTS
The research proj ect has been supported by a National
Science Foundation grant to Agbabian Associates (Grant No.
CEE 77-15010). This support is gratefully acknowledged.
Principal contributors to this work were F. B. Safford and
S. F. Masri. F. B. Safford was responsible for the system
development and the gas pulse generator and S. F. Masri was
responsible for the pulse train algorithm and for the anti
earthquake algorithm. Significant contributions were made by
D.G. Yates in the design of the gas pulser and by B. Barclay in
system development, calibration and test. Other contributors to
the project were Prof. G.A. Bekey of the University of Southern
California, in algorithm development; A.R. Maddox, U.S. Naval
Weapons Center for support and guidance on gas flow in super
sonic nozzles, and J. Sagherian of Agbabian Associates for
reduction of test data.
iv
section
1
2
3
4
5
TABLE OF CONTENTS
INTRODUCTION ...
1.1
1.2
GAS
Background . . . . . Scope of Work. . .
PULSE SYSTEM. . . Gas Pulse System .
Pulse Rocket . . .
Hydraulic Subsystem.
Gas· Storage. Subsystem.
.
Control Microcomputer ..
· · ·
•
. · . · .. · . · . · . ·
2.1
2.2
2.3
2.4
2.5
2.6 Signal Monitoring and Data Processing.
GAS PULSE GENERATOR . .
3.1
3.2
3.3
Design Constraints .
Selection of Rocket Thrust
Variable Thrust. . . . . .
3.4 Thrust Prediction (Programming).
3.5 Safety Features ...... .
MOTION SI~ruLATION BY PULSE TRAINS
4.1 Backgrour:d .
4.2 Pulse Train Development.
4.3 Random Search ..... .
..
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· · ·
· . 1-1
· · ·
· 1-1
1-2
· 2-1
· 2-1
· 2-1
2-5
· 2-8
· 2-12
· 2-12
3-1
3-1
3-3
3-4
3-5
3-8
4-1
4-1
4-1
4-2
4.4 Simulation of Motions Useful for structural Investigations . . . . . . . 4-3
4.5 Performance Characteristics. 4-3
4.6 Impulse and Force Requirements 4-3
4.7 Anti-Earthquake Applications of Pulses 4-6
CALIBRATION . . . . . .
5.1 Machine Operations
5.2 Calibrations ...
5.3 Nozzle Coefficients.
5.4 Thrust Prediction and Test
v
5-1
5-1
5-1
5-3
5-5
R-7824-5489
TABLE OF CONTENTS (Concluded)
section
6 DEMONSTRATION OF MOTION REDUCTION BY PULSES . 6-1
7 DEMONSTRATION TESTS ON A BUILDING . . . . 7-1
8
9
10
7.1
7.2
7.3
7.4
7.5
Objectives . .
Demonstration Configuration.
Specified Pulse Train. .
Tests.
System Performance . .
UTILIZATION
8.1
8.2
Technical Papers .
Dissemination.
RESULTS . .
CONCLUSIONS .
Appendix: PAPERS PUBLISHED AS A DIRECT RESULT OF THIS
7-1
7-1
· 7-1
7-1
· 7-5
· 8-1
. . 8-1
· 8-1
· 9-1
· 10-1
RESEARCH GRANT. ' ................. A-I
vi
R-7824-5489
SECTION 1
INTRODUCTION
A research program was undertaken to validate the applica
tion of pulse techniques for the simulation of earthquake
motions in civil structures. Such a program for on-site exci
tation of civil structures to earthquake motion can provide for
the following needs:
• Adequate experimental justification for complex compu
ter models
• Proof testing of new and rehabilitated structures
• seismic testing of existing structures
This determination of the behavior of structures subjected to
such jolts is accomplished using three-orthogonal-axes earth
quake simulation of civil structures.
1.1 BACKGROUND
Previous analytical and experimental work with mechanical
(metal-cutting) pulse generation indicated that pulse trains
placed at convenient locations on a civil structure could simu
late motion closely approximating earthquake-induced motions.
The simplicity of the pulses (on, off, and amplitude) suggested
that large a..'11ounts of power or energy could be reasonably
handled in a test situation.
The very low periods of large buildings require long dura
tion pulses and high forces. Military and small space rockets
would appear to be an attractive application. Rockets have been
used to measure modal properties by Scruton and Harding (UK) on
a chimmey in 1957, by Corvin and SteiJ1~'1ilber (\-1. Gr.) on a
nuclear power plant contaiG'11ent structure in 1979, and by Sato
and Sawabe (Japan) Oil microlo/ave communications to',vers in 1980.
Trade-off studies were conducted for adaptability of rockets for
pulse train applications. These pulse train studies showed a
need for flexibili~y in thrust magnitude and burn time, both of
1-1
R-7824-5489
which required awkward modifications of the rockets at this
early stage of investigation.
Alternative studies were conducted on variable throat
nozzles and on other forms of propellants such as cold gas,
steam, and hydrazine. From these studies, a nozzle with an
internal metering plug was chosen, and used with nitrogen at a
commercial pressure of 2460 psig as a propellant. This approach
provided the flexibility required in pulse programming but the
thrust levels would be useful only on small structures and large
equipments. The two pulse rockets are pictured in Figure 1-1.
1.2 SCOPE OF WORK
The first maj or phase of this research program was the
development of efficient algori thIns for pulse generation for
earthquake simulation in civil structures and also for the sup
pression or reduction of earthquake-induced structural motions
by counteracting pulses. The second maj or phase involved the
development of the pulse generating system itself, a system that
involved electrical, meChanical, hydraulic and gas dynamic sub
systems. The use of a metering nozzle for variable thrust
control raised questions of thrust efficiency at the onset. A
final phase of the research program included a demonstration
test upon a structure.
This report covers the mal.n development phases of the
research grant. The first sections describe the gas pulse sys
tem (Sec. 2) and the gas pulse generator (Sec. 3). A discussion
of motion simulation by pulse trains is given in Section 4.
section 5 presents data from calibration and initial test runs
of the pulse generators. A demonstration of motion reduction by
pulses (Sec. 6) and a demonstration test upon a structure
(Sec. 7) completes the technical sections of the report. The
final sections discuss a utilization plan and conclusions.
1-2
FIGURE 1-1.
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TWO PULSE THRUSTER UNITS DEVELOPED FOR THIS PROJECT
1-3
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SECTION 2
GAS PULSE SYSTEM
2.1 GAS PULSE SYSTEM
Two gas pulse systems have been developed and are schema
tically illustrated in Figure 2-1. Two independent systems were
produced so as to place each system in opposing directions for
tests of structures or large equipments. This 1I0pposed posi
tioning" permits the sense of positive and negative force
pulses. The operations of the two systems are controlled by a
common microcomputer. Each gas pulse system is composed of the
following subsystems:
o Pulse Rocket
• Hydraulic subsystem
• High pressure gas supply
~ Control microcomputer
In addition, signal monitors and data recordings are pro
vided for. Signal monitoring is particularly critical when the
gas pulse system is used in the anti-earthquake mode (rocket
thrusts to counter structural motions). Moni tor signals of
supply pressure and stroke position requirements of the metering
nozzle of the pulse rockets are used as feedback signals.
2.2 PULSE ROCKET
The pulse rocket is pictured in Figures 2-2 and 2-3, and
schematically shown in Figure 2-4. The pulse unit mounted upon
a hydraulic actuator is 55 in. in length and weighs 500 lb.
Thrust amplitudes are controlled in the on-state by positioning
the metering plug for the required throat area in G~e nozzle for
flow control. The off-state for the pulse occurs by signaling
the hydraulic actuator to move the metering plug to seal off gas
flow at L~e nozzle.
Nominal thrust or output force with gas supply at initial
pressure is 10,000 lbf. The convergent-divergent nozzle is the
2-1
GAS SUPPLY STORAGE 6 K BOTTLES
2640 PSI
SIGNAL HON ITOR
• OUTPUT FORCE • SUPPLY PRESSURE L---.! • STROKE POSITION ~ • INPUT SIGNAI.S
ACCUMULATOR 3000 PSI, 10 GAL
HYORAUL I C PUMP
GAS SUPPLY STORAGE 6 K BOTTLES
2640 PSI
SIGNAL MONITOR
• OUTPUT FORCE
LOAD CELL
• SUPPLY PRESSURE -----l • STROKE POSITIOH ~ • INPUT SIGNALS
HYDRAULIC ACTUATOR
,~ -@-----
TO SECOND PULSE SYSTEM
ROCKET
} FROM SECONO
'----- PULSE SYSTEM
HYDRAULIC ACTUATOR
-@-----
INPUT PULSE TRAI N PROGRAMS
/ROCKET
r->--'--r-1
LOAD CELL/f
ACCUMULATOR 3000 PSI, 10 GAL
TO SECONO PULSE SYSTEM
} FROM SECOND
'----- PULSE SYSTEM
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PULSE UNIT NO. 1
SIGNAL CONTROLLER
COMPUTER
PULSE UNIT NO_ 2
SIGNAL CONTROLLER
« --. Q
AA6i2
FIGURE 2-1. SCHEMATIC OF TI'iO GAS REACTION PULSE-GENERATI~G SYSTEMS CONTROLLED BY CENTRAL HICROCOMPUTER
2-2
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R-7824-5489
AIR SUPPLY HOSES
FIGURE 2-3. FRONT VIEW OF GAS PULSE GENERATOR
--~~~-------
.. IIDGIWI_-----~ SIGIIALS AA610
FIGURE 2-4. GAS REACTION FORCE PULSE GENERATOR EQUIPPED WITH A 90-GPM SLAVE VALVE AND A 5-GPM PILOT VALVE
2-4
I I I I I
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R-7824-5489
De Laval type and is 8.2 in. in length, with a 2-in.-dia. throat
and a 6.78-in. exit diameter. This configuration gives a cone
angle of 32.5 deg and an efficient flow of 98% (2% loss by
divergence) . The plenum chamber behind the nozzle houses t..~e
metering shaft, gas seals, and air supply hose connections. The
chamber is 9 in. long and 8 in. rD.
2.3 HYDRAULIC SUBSYSTEM
The function of , the hydraulic subsystem, upon command from
a microcomputer, is to position the metering plug in the gas
rocket. This subsystem consists of a hydraulic actuator,
hydraulic power supply, power control panel and signal con
troller.
The hydraulic actuator is pictured in Figure 2-2 and sche
matically in Figures 2-1 and 2-4. This actuator has an output
force of 6,600 lbf and a stroke of 2 in. Overall dimensions are
24 in. in length and 6.3 in. body diameter. Two units were
acquired from L~ng Electronics.
The force-output rating of the actuator was selected on the
basis of the total mass to be moved (metering plug, shaft, and
hydraulic piston) and the gas pressures in the plenum chamber of
the rocket. High output force is required for rapid opening and
closing of ~~e metering plug. To improve rise times, oversized
hydraulic pilot valves (5 gpm) and slave valves (90 gpm) are
used. Rise times less than 13 msec have been achieved.
The hydraulic power supply is given in the schematic of
Figure 2-5. The principal energy source is the 10 gal accumu
lator which is used to drive the actuators. The accumulator has
sufficient capacity for most earthquake applications and thereby
eliminates the need for a high cost hydraulic pump. A small
hydraulic plli~P (5 gpm) proved adequate to bring the subsystem UD
to operating pressure (3000 psi) and sustain the leakage flow In
the actuator because actuator leakage occurs in both slave and
pilotvalves and in the hydrostatic bearings. One of the 10 gal
accumulators is pictured in Figure 2-6.
2-5
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R-7824-5489
FIGURE 2-6. 3000 PSI HYDRAULIC ACCUMULATOR USED AS POWER SOURCE FOR HYDRAULIC ACTUATOR
FIGURE 2-7. -CONTROL CONSOLE FOR TWO HYDRAULIC ACTUATOR SYSTEMS. TOP TWO PANELS ARE SERVOCONTROLLERS FOR EACH ACTUATOR. BOTTOM PANEL IS HYDRAULIC PUMP CONTROL.
2-7
R-7824-5489
Operation of the hydraulic power supply is performed by
control electronics to power up the system to pressure and
includes override and interlocks for temperature and fluid
levels. Command of the hydraulic actuator is through the servo
controller. Two of these units are pictured in Figure 2-7.
These units receive input commands from the microcomputer by
which _each servo controller operates an actuator. Feedback
signals_ from pressure differentials, servo valve position and
actuator position provide accurate response to the input sig
nals. Schematics of the hydraulic servo and servo controller
are-qiven in Figures 2-8 and 2-9 .
... To assure safety, all- pipe fittings , valves, and hoses are
rated . at 12,000 psi burst pressure. The hydraulic system
~perates under pressure at 3000 psi.
2.4 GAS STORAGE SUBSYSTEM
Gas supply storage for nitr~gen gas consists of six stan
dard industrial high pressure tanks, four 10 ft long 1-1/4 in.
dia. flexible hoses and the plenum chamber for each gas pulse
generator system. Three pressure tanks are mounted as a group
with each tank equipped with a valve and a manifold. A typical
unft is pictured in Figure 2-10. Gas capacity for each puls~.
unit is as follows:
Unit Element No. Volume Volume
Tanks 6 2,661 15,966
Hoses 4 212 848
Manifolds 2 105 210
Plenum 1 511 511
17,535 in3
(10.2 ft3 )
For each unit, this amounts to 134 lb of nitrogen compressed at
2640 psig.
2-8
j~'~ R-7824-5489 ,(tt ~, I," ',.
COMMAND SOURCE
. ~,
SERVOVALVE COMMAND SERVOCONTROllER
~-~ HYDRAULIC ACTUATOR .:~ A ~
ITt SERVOVALVE LVDT (AC)
l DIFFERENTIAL PRESSURE TRANSDUCER (DC) ///'//////////'//
ACTUATOR LVDT (AC)
FIGURE 2-8. HYDRAULIC SERVOCONTROL BLOCK DIAGR~~ FOR HYDRAULIC ACTUATOR
2-9
COMMAND
-LIMIT +lIMIT
10 CONTROL PANEL LOGIC
L--~ I I I I
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Q ACTUATOR LVOT
MONITOR G LOAD CELL
DISPLACEMENT '
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METERI DAMPING
D.C. BIAS
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CARRIER
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TO SERve VALVE
SLAVE VAlVE
r------~ LVDT
esc I LLATOR 1-------. 10 KHZ
ACTUATOR LVDT
_ _ LOAD IOC SUPPLY r-------<"J CELL
I DC SUPPLY 1-1-----4
AA608
FIGURE 2-9. SERVO CONTROLLER BLOCK DIAGRN1 FOR HYDRAULIC ACTUATOR
2-10
R-7824-5489
~~
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FIGURE 2-10. HIGH PRESSURE GAS STORAGE UNITS (ONE SET OF FOUR) USED TO SUPPLY PULSER
2-11
R-7824-5489
2.5 CONTROL MICROCOMPUTER
The microcomputer controls the firing pulses for both pulse generating systems. This computer, a PDP 11V03L, manufactured by the Digital Equipment Corp., is pictured in Figure 2-11, and its main features are diagrammed in Figure 2-12. Operat:.i_~~of
the pulse generator requires that both pulse generating and. counter-motion algorithms be programmed in machine language (real time).
Four channels are available for output via a D/A converter, and these are used in channel pairs for valve position and time commands to each pulse generator (hydraulic servo controller). Sixteen system channels are available for input via AID converter to receive input signals of dynamic response of structures. These input or feedback signals are used by the anti-earthquake algorithm to initiate pulses at appropriate~time durations and amplitudes to reduce structural motions that would be caused by an earthquake.
programming for earthquake testing is straightforward. A test program is initiated and the valve position (amplitude) and the qn/off times are entered for each pulse unit from the keyboard. The desired pulse program is stored in memory and upon call-up will initiate the pulse firing sequence.
2.6 SIGNAL MONITORING AND DATA PROCESSING
Performance of the gas pulses is monitored and recorded as functions of time by the following:
e Metering nozzle position - Hydraulic actuator LVDT.
e· Plenum chamber pressure - Pressure transducer Teledyne model 206AGX, 0-3000 psig.
• Thrust - Load 0-25,000 lbf.
cell Interface model
• Command pulse train - Direct recording signals.
2-12
1220AF,
Reproduced from best available copy.
R-7824-5489
FIGURE 2-11. CONTROL MICROCOMPUTER (LEFT) AND DATA RECORDING AND PROCESSING SYSTEM (CENTER AND RIGHT)
2-13
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R-7824-5489
These recorded signals permit a quick assessment of performance
and a means of determining the nozzle coefficient from
where
CFX = Nozzle coefficient
F - Rocket thrust, lbf
At = Throat area, . 2 l.n
Pc = Chamber pressure, pSl.a
Several methods are available for recording test results.
The method used in this report is by signal capture via an l"\/D
converter into circulating registers. Subsequent processing on
digital data acquisition/processing equipment is performed
wi thin a few minutes after testing i the Zonic equipment used
for this procedure is pictured in Figure 2-11. Data displays
are in time histories and Fourier spectra. Eventually, data is
transferred to a main-frame computer for time series analysis.
2-15
R-7824-·5489
SECTION 3
GAS PULSE GENERATOR
The design of the cold gas generator involved not only its
performance but safety as well, especially in view of the high
pressure storage capacity.. flexible hose links, pipe fittings I
and the pulse rocket. Pictures of the two pulse rockets mounted
on their hydraulic actuators are shown in Figure 1-1.
3.1 DESIGN CONSTRAINTS
A major constraint in the design of the gas pulse generator
was the selection of the internal gas pressure. The setting of
maximum pressure levels was determined by safety considerations
and t..'le availability of standard pipe fittings and hoses and
commercially available high pressure nitrogen tanks. These
considerations set the nominal. operating gas pressure of the
system at 2640 psig (standard commercial K size gas storage
bottle 1.54 ft3 ). Commercial pipe fittings and hoses have burst
pressures of 12,000 psig. With 2640 psig as nominal, a maximum
value of 3000 psig can be used when high thrusts are required.
A secondary design constraint was the internal pressures
upon the metering plug. As can be observed in Figure 3-1, when
the plug is in the closed position (no flow) the projected flat
plate area times the internal chamber pressure (Pc) presents an
initial force which must be overcome by the hydraulic actuator.
This force, plus the reaction forces of the masses of the meter
ing plug, shaft, and actuator piston, controls the opening time
of the pulser. Closing, as from a full open position, also
includes a side-on gas pressure at the front of the metering
plug, but this is a lesser force than above. A pressure balanc
ing piston ,.;as added to compensate for L'1e pressure forces on
the rear of the metering nozzle. This device promotes a more
rapid opening. The piston, as can be seen in the sketch of
Figure 3-1, is actuated by a step in the shaft for nozzle posi
tion of 0 to 0.25 in.
3-1
STEPPED SHAFT
R-7824-5489
,,--.... ;' ....
-"
RETRACTED POSITION
(a) Metering nozzle and pressure balance piston configuration
0.5 1.0 1.5
METERING NOZZLE POSITION, in.
(b) Calibration curve
2.0
FIGURE 3-1. THROAT AREA (ANNULUS) AS A FUNCTION OF METERING NOZZLE POSITION
3-2
AA557
AA556
These design limits set the requirements of
actuator at 6,600 Ib output force and the throat
of the De Laval nozzle at 2 in. (At = 3.14 in2 ).
3.2 SELECTION OF ROCKET THRUST
R-7824-5489
the hydraulic
diameter (dt
)
The maximum thrust of the rocket (metering plug in fully
retracted position) can be established by the following:
where
F = Rocket ,thrust, Ibf
Pc = Chamber pressure, psia = 2143 + 14.7 = 2157.7 psi a -At = Throat area, in2 = 3.14 in2
CFX = Nozzle coefficient = A~CF
where
A = Flow divergence factor in superson~c section = 0.98
~ = Friction loss factor =0.95
CF = Lossless nozzle coefficient
Hence, F = 6300 CF .
Flow divergence in the supersonic section of a nozzle lS
related to the cone angle by
A = ~ (1 + cos a)
where
a = 1/2 nozzle exit cone
Good design sets A at 0.98, and this results In an exit cone
angle of 32.5 deg (hence, a = 16.25°) such that the exit area of
the cone is A = 36.1 in2 (d = 6.78 in.). e e
Friction loss factor Il = 0.95 is empirical. The lossless
nozzle coefficient is found from the following:
3-3
R-7824-5489
2 y - 1
where
y = Ratio of coefficients of specific heat, for N2 = 1.41
Pe = Pressure at exit plane of nozzle
Pc = Chamber pressure
Po = Atmospheric pressure
Ae = Area at exit plane of nozzle
At = Throat area
For full expansion at the nozzle exit plane, P e = Po and
maximum thrust occurs for the design chamber pressure
CF = 1.577
and
design thrust
F = 10,000 lbf for 2460 psig static storage pressure
3.3 VARIABLE THRUST
Thrust may be varied by commanding the position of the
metering plug from the closed (no flow) position to the full
open (maximum flow). On command from a signal programmed in the
microcomputer, the metering plug retracts to a specified posi
tion, at which point the throat area is an annulus between the
conic surface of the metering plug and the wall of the conver
gent section of the nozzle. Figure 3-1 shows the functional
relation between the retracted position of the metering plug and
the throat area, At'
Loss in thrust efficiency will occur with small throat
areas due to over-expansion of the flow at the exit plane of the
3-4
R-7824-5489
nozzle. Addi tionally, secondary shocks at the apex of the
metering plug, compression shock, and turbulence will combine to
reduce efficiency. For practical applications, the nozzle
coefficient CFX must be calibrated for a range of chamber pres
sure, throat area, and thrust, using L~e relation
c = FX. ~
F. ~
3.4 THRUST PREDICTION (PROGRAMMING)
The present gas storage capacity for each pulse generator
consists of six gas bottles, four 10 ft long hoses, and the
plenum cha~er of the gas rocket. This storage capacity amounts ~
to 10.2 ft ..... , and 134 lb of nitrogen compressed at 2640 psig.
After each pulse, the stored gas is reduced in pressure, and
hence, less potential energy. Thus, to program a pulse train, a
series of incremental solutions to the gas equations are
required. For example, chamber pressure of 2640 psig can reduce
to 400 psig and internal energy would reduce thereby from
134 Btu/lb to 119 Btu/lb after the last pulse. At the beginning
of each pulse, the state of the pressure, internal energy,
temperature, and weight of gas (reservoir) must be k..'l.O'.offi in
order to program the ne:~t pulse for thrust, by the' throat area
and the calibrated nozzle coefficient. An example of these
calculations is given in Table 3-1.
Thrust is given by
F = - m V + A (P - P ) xe e e 0
where
F = Thrust, Ibf
rn = Mass rate of flow, Ib-sec/ft
Exit of nozzle, 2 A = area lD
e
Pe = Exit pressure, pSla
p = jI..mbient pressure, psia "0
3-5
w I m
Pu
lse
No.
1 2 3 4 5 6 7 8 9
10
Req
'd
Fo
rce
1,2
30
84
7
4,3
32
2,7
42
1,1
05
2,0
78
2,3
48
3,5
54
1,4
00
30
2
TABL
E 3
-1.
EXA
MPL
E O
F IN
CREM
ENTA
L C
ALC
ULA
TIO
NS
NEE
DED
TO
E
STA
BL
ISH
V
ALV
E PO
SIT
ION
FO
R TH
RU
ST
REQ
UIR
EMEN
TS
Ple
num
Cha
mbe
r W
eig
ht
Jet
Sto
rag
e C
ap
acit
y
Rat
e o
f V
elo
cit
y
Sta
tic
Tra
nsi
en
t F
low
Val
ve
po
siti
on
P
sta
rt
Pen
d
Pc
Sta
rt
Sto
p
nif
f.
V
w
ex
W
W
l!.W
. 2
(psi
g)
(psi
g)
(psi
g)
(lb
) (l
b)
(lb
) lb
/sec
ft/s
ec
in.
~n
0.1
2
0.4
4
2,2
00
2
,15
7
2,1
45
1
11
.87
ll
O .3
2
1.5
5
18
.3
2,1
61
0.1
0
0.3
4
2,1
57
2
,12
7
2,0
99
ll
O.3
2
10
9.3
1
.07
1
2.6
8
2,1
49
0.4
6
1.6
3
2,1
27
1
,98
5
1,8
12
1
09
.3
10
4.1
5
.2
66
.1
2,1
09
0.3
0
1.1
2
1,9
85
1
,89
6
1,7
93
1
04
.1
10
0.8
3
.3
41
.63
2
,11
9
0.1
3
0.5
1
1,8
96
1
,87
6
1,8
28
1
00
.8
10
0.1
5
0.7
5
16
.7
2,1
24
0.2
3
0.8
8
1,8
76
1
,81
0
1,7
16
1
00
.05
9
7.5
4
2.5
1
31
. 5
2
2,1
21
0.2
9
1.0
8
1,8
10
1
,73
5
1,6
58
9
7.5
4
94
.68
2
.86
3
5.6
3
2,1
20
0.4
5
1.6
0
1, 7
35
1
,62
5
1,5
42
9
4.6
8
90
.45
4
.2,3
5
4.1
3
2,1
12
0.2
0
.75
1
, 6
25
1
,58
3
1,5
37
9
0.4
5
88
.8
1.6
5
21
. 53
2
,09
2
0.0
5
0.1
8
1,5
83
1
,57
4
1,5
56
8
8.8
8
8.4
3
0.3
75
4
.64
2
,09
3
Den
sity
w
lbs/f
t3
10
.97
10
.86
10
.13
9.7
1
9.5
3
9.1
7
8.8
1
8.4
5
8.2
7
8.2
0 -~
'-- ~
:u I '" 00 N
.t>
I lJ1
.t>
oo
I.D
R-7824-5489
For these calculations P e = Po was assumed, with subsequent
correction made using the calibrated nozzle coefficient CFX '
For the jet velocity,
. where
J... = Nozzle divergence factor = 0.98
V = Jet velocity, ft/sec e
V = lv-\)(:~)~ _(~~)'r/2 e
where
= Gas density in 24 Pc chamber, lb-sec /ft
Other parameters as given before.
The mass flow through nozzle is
where Ac is the acoustic velocity (ft/sec) In the chamber and is
given by:
A ~ ~Y Pc c v P
plus temperature correction . c
Other parameters have been defined previouslY.
From the general flow equation and for the condition of no
flow, the chamber pressure is given by:
+ U = constant c
3-7
where
Vc ::: Specific volume, ft3/lb
Uc ::: Internal energy, Btu/lb
J ::: Heat equivalent of work, 778 ft-lb/BTU
R-7824-5489
Flow occurs upon retraction of the metering plug, which
results in a drop in chamber pressure (Pc)' This quantity is
required to predict thrust:
and
...:L
Pt = (Y ~ r-1 1 Pc = 0.53 Pc
'" ~~ 0.53 Pc
V t '" Pt
where
v c' v t ::: Specific volumes at chamber and throat, ft3/lb
Pt ::: Density at throat, lb-sec2/ft4
Pt ::: Pressure at throat, psia
Vt = Velocity in throat, ft/sec
3.5 SAFETY FEATURES
The structure of the pulse rocket was designed with safety
as a principal consideration. Major elements were the end caps,
cylinder, and tie rods.
o End Caps. Stress including preload from the 4 tie
rods was less than 20,000 psi.
Tie-rods. 1-1/4 in. diameter, AISI 1045 cold drawn
steel, 100 I 000 psi yield strength. stressed to
41,000 psi.
3-8
•
R-7824-5489
Cylinder (Plenum Chamber). 8 ~n. ID, 3/8 in. thick
wall, 9 in. long. Material AISI 1026 heat treated to
118,000 psi tensile stress. Worse case hoop stress
45,000 psi.
3-9
R-7824-5489
SECTION 4
MOTION SIMULATION BY PULSE TRAINS
4.1 BACKGROUND
Simulation of structural motions by a series of pulses in
order to match motions induced by man-made-or natural events was
undertaken in 1973. The motivation for this effort was the need
for test and experimental information, particularly about
motion-time histories of large and massive structures as they
can be expected to react to future catastrophic events.
These studies demonstrated that the pulse trains could be
all in one direction of a single axis if desired or necessary,
or could be in either direction. A pulser performs only three
functions: on, off, and magnitude. This simplicity is essential
for controlling large amounts of energy.
4.2 PULSE TRAIN DEVELOPMENT
The development of a pulse train to replace an earthquake
or other events for testing or experiment is illustrated in
Figure 4-1 below:
INPUT
EARTHQUAKE
OR
OTHER EVENT
~ TRANSFORJIATION
ANO
RELOCATION OF INPUT
I -"
B= PULSE TRA I N
x STRUCTURAL DYNA,~ Ie
CHARACTERISTICS
i
f T
STRUCTURAL
X JYNAMIC
CHARACTE?-I STI C S
FIGURE 4-1. USE OF PULSE TRAINS TO OBTAIN EQUIVALE}IT STRUCTURAL RESPONSES TO EARLqQUAKE OR OTHER EVENTS
4-1
R-7824-5489
The transformation and relocation function in Figure 4-1
changes the continuous ground motion of an earthquake, to a
series of discrete pulses placed on a structure or building at
locations of test convenience. The response due to pulses is
approximate to the criteria or objective response. Computer
studies have shown this approximation can easily be held to
about a 5% error level over the motion-"time history. This
error can change in actual tests due to the dependence on the
performance of pulse excitation devices.
The determination of pulse trains is made by successive
iterations using a general purpose computer. The algorithm
developed for this research project is described and detailed by
Masri and Safford in "0ptimization Procedure for Pulse-Simulated
Response, II which is reprinted in the Appendix. The three para
meters for each pulse (on, off, and magnitude) and for each
pulse train location, p·otentially require an extremely large
number of iterations for convergence to a global m1n1mum.
Algorithms using conventional convergence methods require exces
sively long run times. The difficulties encountered in obtain
ing convergence required the development of an algorithm which
employed random search techniques.
4.3 RANDOM SEARCH
A new random-search global optimization algorithm was
developed in which the variance of the step-size distribution is
periodically optimized. By searching over a variance range of 8
to 10 decades, the algorithm finds the step-size distribution
that yields the best local improvement in the criterion func
tion. The variance search is then followed· by a specified
number of iterations of local random search where the step-size
variance remains fixed.
introduced to ensure that
minimum. This algori th'1l
Periodic wide-range searches are
the process does not stop at a local
is the basic building block for the
specialized pulse algorithm presented in the appendix and is
listed in the bibliography by f1asri et al. I "A Global Optimiza':"
tion Algorithm Using Adaptive Random Search."
4-2
R-7824-5489
4.4 SIMULATION OF MOTIONS USEFUL FOR STRUCTURAL INVESTIGATIONS
Emphasis in simulation has been placed upon simulating
earthquake motions in structures. However, the pulse method is
sufficiently versatile for L1.e inducement of other types of
motion. As can be seen in Figure 4-2, sinusoidal motion can be
developed. Other studies have sho'Nn that random vibrations can
also be generated. Housner in 1946 (see Bibliography) showed
that base motion input of pulses with random amp Ii tude could
represent the effects of earthquakes on dynamic systems. Single
pulse or multi-pulse tests can also be used to obtain transfer
functions of structures and for extraction 6f modes.
4.5. PERFORMANCE CHARACTERISTICS
Studies of the ratio of the time duration of dynamic motion
of a structure t~ the sum of the pulse times varies from 3 to 1
to 5 to 1 for each point of input. A pulse train developed fer
a specific structure is not unique, for a generally appearing
different pulse train will produce the same result. This non
uniqueness permits development of pulses more compatible to the
performance of excitation devices. Experience has also shown
that the structural response is somewhat insensitive to errors
in the pulse train amplitudes.
4.6 IMPULSE AND FORCE REQUIREHENTS
Operations with the algorithm for pulse generation have
also disclosed a need for secondary optimization for minimiza
tion of impulse and force requirements. Table 4-1 covers
average requirements for a pulse train as well as total impulse
required for application to a 25-story building. Applications
of pulse excitation on the 33rd floor requires average
forces for 18 pulses of 1.9 million lb and a total impulse of 23
million lb-sec. This study on the 25-story building was one of
the first made and very little interactive effort was employed.
4-3
23
• t
13
(a) Model
:: o. 08
o tit V V
(c)
to"\ o
TIME, s
Displacement, Floor 23
O. 12 r---,---r--r--....... ~-"T""---r---,
0.08 I-
- 0.04 J
: o~~~n~~+H~H+~---~ ~-0.04 q~ ...J
~ -0.08
-0.12~~~_~~~_~~-...J
o 4 8 12 16 20 24 28 32 TIME, s
(e) Velocity, Floor 23
NO 0 . 08 r--....--...,..-r--r---,.--r---.----.
x 0.06
.::. 0.04
5 0.02 ~ ~ O~rrr~~~H*H+-----~ UJ
u:: -0.02 u ~ -0. 04 L-....I---L. __ J...--'-......J. __ '"--~-...J
o 4 8 12 16 20 24 28 32 TI ME, 5
(g) Acceleration, Floor 23
R-7824-5489
6r-~-r~~~~~~~
UJ U
4
2
~ 01'-n"'T":r.,....,,.,...,1I""'T'''r.m.;w..----j u..
-2
-4 -6~~~~~~~~~
o 4 8 12 16 20 24 28 32
...::'0 0.12
x 0.08 ~
N 0.04
~ 0 UJ ::t: ~ -0.04 < c: -0.08 V'>
;; -0.12 o
TIME, s
(b) Pulse train
A r 'VV
4
~ I !
Ij 8 12 16 20 24 28 32
TIME, s
( d) Displacement, Floor 13
o . 06 .---r--,.--,.---,----.-..,.---,-~
0.04
0.02 x
~ O"'IVv ~ -0.02
...J
~ -0.04
to"\ 0
x ~
N
-0.06L-....I---L._J...--'-......J. __ '"--~-...J o 4 8 12 16 20 24 28 32
TIME, s
(f) Velocity, Floor 13
0.32
0.24
0.16
:z 0.08 o ~ < a: ~ -0.08 UJ U ~ - 0 . 1 6 L-....I---L. __ "'---'---l. __ '"----'--...J
o 4 8 12 16 20 24 28 32 TIME, 5
(h) Acceleration, Floor 13
FIGURE 4-2. COMPARISON OF EXACT AND PULSE SIMULATED ---e----B- i-10TIONS OF 25-DOF BUILDING. CRITERIA INPUT IS SINUSOIDAL EXCITATION OF FLOOR 23. PULSE TRAIN ALSO APPLIED TO FLOOR 23.
4-4
R-7824-5489
By placing the pulse units at four different floors, average
force dropped to 470,000 lb and total impulse to 8.8 million
lb-sec.
TABLE 4-1. PULSE TRAIN REQUIREMENTS TO EXCITE 25-STORY OFFICE BUILDING TO EL CENTRO 1940 EARTHQUAKE
No. of Average Average Total Pulse Unit Pulse Location Pulses Duration, Force, Impulse,
Req'd Sec lbf lb-sec
23rd floor only 18 0.784 1.91 x 106 23.44 x 10 6
23rd, 18th, 13th 52 0.41 0.47 x 106 8.849 x 10 6
and 8th floors (13 per floor)
Table 4-2 covers the pulse train requirements for a 3-story
test structure located at the Earthquake Engineering Research
Center, University of California, Berkeley. This table is
useful in comparing force and impulse requirements for various
placements of pulse units. This latter application resulted
from improvements to the algori thrn and from more interactive
efforts.
TABLE 4-2. PULSE TRAIN REQUIREHENTS TO EXCITE 3-STORY UeB TEST STRUCTURE TO EL CENTRO 1940 EARTHQUAKE
No. of Average Average Total Pulse Unit Pulses Pulse Force, Impulse,
Location Duration, Req'd Sec lbf lb-sec
3rd floor only 23 0.100 1,882 4,324
2nd floor only 23 0.083 4,076 6,906
1st floor only 24 0.077 6,387 10,704
All floors 75 0.048 4,507 9,5-'-l5 (25 per floor)
4-5
R-7824-5489
4.7 ANTI-EARTHQUAKE APPLICATIONS OF PULSES
It is possible, using the information from the above dis
cussion, to show that a pulse generating system could be used to
reduce structural dynamic motions by firing the pulses to oppose
the earthquake motions of a building. An array of transducers
would be required in the building to sense- acceleration, velo
ci ty, displacements, and/or strain. An on-line computer to
receive and process these feedback signals in real time would be
used to counterfire the pulse units at the proper time phasing,
time duration, and amplitude.
An on-line pulse control algorithm was developed for use
with distributed parameter-structures and for arbitrary disturb
ances. This effort was part of the research grant. This algorithm was programmed in machine language for the DEC PDP
11V03-L microcomputer (described earlier in Sec. 2). This
computer is equipped with 16 signal channels via A/D conversion
for transducer feedback and 4 command channels from the computer
via D/A conversion to control the pulses. A more complete
description of this anti-earthquake system is in the reprint of
the paper given in Appendix A.
This anti-earthquake study must be viewed at this time as
an exploratory study. Eventual applications to large buildings
will require a careful evaluation of pulse system reliability
and pulse forces required. The high reliability and low costs
of integrated circuits permit large redundancy for the processed
sensor data, readiness status checks, and voting logic. In
addition, redundant motion sensors would be used. Pulses would
be sized for force output and pulse durations to operate only
when the building motion exceeds potentially damaging or life
threatening thresholds (i.e., motions beyond the seismic resis
tance of the building). Force-time requirements would requlre
pulses to be in the form of solid propellant rockets.
4-6
R-7824-5489
SECTION 5
CALIBRATION
Calibration and initial test runs were performed to estab
lish nozzle coefficients and operating characteristics of the
pulse generators. A complete matrix of t~sts was not performed
for the full range of chamber pressures and metering nozzle
positions due to program limitations.
S.l MACHINE OPERATIONS
Numerous tests were made upon the hydraulic actuator to
optimize feedback for maximum rise time of the hydraulic piston
to step and pulse function commands. A series of calibrations
was also performed on the LVDT of the piston shaft for use in
establishing metering nozzle position (throat area).
During these operations, the only maj or failure of the
system occurred with the galling of the aluminum shaft of the
metering nozzle. Galling occurred between the shaft and its
housing in the base· block of the plenum chamber. Shafts from
each unit were re-machined and shrink-fitted with 0.10 in. thick
wall steel tubing.
unit.
Grease fittings were also added to each
5.2 CALIBRATIONS
The following four signals were used for calibration and
measurement of pulse performance:
• Input signal from computer (in./volt)
• Metering plug position LVDT (in./volt) for throat area
• Chamber pressure (psig)
a Output thrust (lbf)
The phase relationships between these several signals are dis
played in L~e overlay plot of Figure 5-1. Studies were made for
5-1
R-7824-5489
~_+--_~/~+--__ -l1~1 J J ~ ~UT?UT FORCE, LOAD CELL
~--+--I'~a,q;;/~\~"V,...J..""'-7~METERING PLUG (POSITION) LVDT
I \A /COMPUTER INPUT SIGNAL, ---p.---4-----l
"'-"-- I -)? r ""\ VCHAMBER PRESSURE
" I \1\,.1 \( V " ./-
II'!... \liV -
I 1 \ 11
o 0.2 0.4 0.6 0.8 0.10 0.12 0.14 0.16 0.18 0.20
TIME, sec
FIGURE 5-1. OVERLAY OF TIME HISTORY DATA MEASURING PERFORMANCE OF A PULSE UNIT AND SHOWING PHASE RELATIONSHIPS
10,000 1.0 I T
.....
.c --UJ u a: 0 0 ..... l-=> ~ l-=> 0
-10,000 o
INPUT VOLTAGE ~OUTPUT FORCE II CONTROL SIGNAL I
/ .A ~ I , I
I PULSE LIDTH 1/
120 msec
I
0,1' -. RISE TIME 13 msec .... 1;/
r-- DELAY TIME 13 msec
20 40 60 80 100 120
TIME, msec
"'·T, 1\(1 )
-x.. '\
<J1 ....
1\ "0 >
\ 'SURGE -tPNEUMATI C
-I
\ ~ l:.., .... y \/ '\....I .......
I U, ,~ I
/' " HY DRAULI C
'-/ CONTROL
REACTANCE
140 160 180
-' < Z <.:J -Vl
0 -' 0
"" r-z 0 w
l-=> a.. z -
- 1.0 200
FIGURE 5-2. PHASE RELATIONSHIP INPUT SIGNAL FROM MICROCOMPUTER AND OUTPUT FORCE
5-2
AA615
R-7824-5489
the phase relationship between input voltage signal and output
thrust as shown in Figure 5-2. Delay time between the onset of
the input signal and 50% level of maximum for the thrust was
13 msec. Rise time of thrust from 10% to 90% of maximum was
also 13 msec.
5.3 NOZZLE COEFFICIENTS
Nozzle coefficients were determined from the following
relation:
where
F
=
= Thrust, lbf
. 2 = Throat area, ~n.
= Chamber pressure, psia
The predicted nozzel coefficient, which includes the exit velo
city divergence factor and a function loss factor, was given as
1.47 (see Sec. 3). Data from tests showed a variation in nozzle
coefficients, which were somewhat independent of chamber pres
sures but were directly affected by pneumatic surges in the
plenum chamber, hoses, and storage tanks. This surging may be
observed in Figure 5-3, which plots both thrust and chamber
pressure as a function of time. Surge periods are a function of
chamber pressure/ranging from 51 msec (19.6 Hz) at 2500 psig to
62 msec (16.1 Hz) at 1000 psig. Evaluation of data showed a
relation of the nozzle coefficient to the ratio of pulse dura
tion to surge period. For pulse duration longer than the surge
period, unstable flow results with a consequential reduction in
thrust. Table 5-1 lists the effects of pneumatic surge upon
nozzle coefficients.
5-3
VI I ,(
0.
-t=
t-
--~--~-b
.-
-::c
:I -r
E
:: J.
:t
__ ..-.
::-_
~I
~ J
~ ~r
l 2
52
0 ~~
~~h-69~ I
b -
6044
Ib
e-r
53
03
Ib
-46
88
Ib
r-
4219
Ib
' .-
3797
Ib
r
3563
Ib
--3
188
Ib
=
. I
\1 'A
~
=
"'~
~-H
P"
r::-1
--:'
;--~-1
iL
-' T_
-i
" -I
=-~I
,-
F--l-
+-.
.c:\
J
11
~-:._
c-
P;:;::
I -
"I.
I'.
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TABLE 5-1. EFFECT OF PNEUMATIC SURGE ON NOZZLE COEFFICIENTS
Pneumatic Ratio:
R-7824-5489
Nozzle Duration, Surge Period, Pulse Duration Coefficient,
msec msec Surge Period CFX
46 56 0.8 1.50
55 56 1.0 1.37
73 56 1.3 1.36
89 56 1.6 1.18
5.4 THRUST PREDICTION AND "TEST
Prediction of thrust is given by
. F ~
W AVe = g
where
F = Rocket thrust, lbf . W = Flow rate, lb/sec
Ve = Jet velocity, ft/sec
A = Nozzle divergence factor, 0.98
~ = Pneumatic surge factor
I
Except for the pneumatic surge factor, the above parameters are
covered in more detail in section 3. The pneumatic surge factor
is the ratio of the empirical nozzle coefficient (when surging
is present) and the calculated nozzle coefficient. For the test
data for the 9-pulse test shown in Figure 5-3,
~ CFX ( exn) 1.36 0.925 = = 1.47 = CFX(calc)
and
. F 0.907 W
V = -g e
5-5
R-7824-5489
Calculations and test data are shown in Table 5-2. The average
difference between predictions and test data for thrust is 1.8%.
TABLE 5-2. COMPARISON OF CALCULATED THRUST TO THRUST TEST DATA FOR 9-PULSE TEST OF FIGURE 5-3.
Calculation Test
Flow Exit Thrust Thrust Pulse R~te Velocity F, F, Difference, No. W, Fe' lbf lbf %
lb/sec ft/sec
1 138.0 2066 8035 7875 2.0
2 124.0 2018 7052 6938 1.6
3 110.0 1964 6089 6094 0.1
4 100.0 1921 5414 5303 2.1
5 91.0 1877 4814 4688 2.7
6 83.6 1837 4328 4219 2.6
7 77.3 1807 3937 3797 3.7
8 71.1 1772 3551 3563 0.4
9 65.5 1736 3205 3188 0.5
5-6
R-7824-5489
SECTION 6
DEMONSTRATION OF MOTION REDUCTION BY PULSES
A demonstration of motion reduction by pulsers was
accomplished using an analog computer to model a three-story
moment-resisting frame structure (test structure at the
University of California, Berkeley). Base motion to this
structure employed a random noise generator for the analog
computer. The algori thm developed for motion reduction was
employed with the DEC PDP 11V03L microcomputer shown in Fig
ures 2-1 and 2-11. The analog computer used in this study is
shown in Figure 6-1. This demonstration was accomplished
on-line in real time.
The effect of anti-earthquake pulse control on the 3rd
floor velocity and displcement of the UCB test structure is
shown in the analog data traces of Figure 6-2. In this figure 1
the effect on motions of the structure with or without pulse
control can be observed in the data records. The counteracting
pulses may be triggered at crossings of specified thresholds.
Figure 6-3 illustrates the rms velocity levels attained for two
different thresholds with respect to "no pulse" control. A more
elaborate data display of acceleration, velocity and displace
ment for the 3rd floor of the analog of the UCB structure with
respect to the countering pulse train is presented by the data
of Figure 6-4. Demonstrations using the gas pulsers for motion
suppression on a structure were not made due to funding
limitations.
6-1
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R-7824-5489
~ I I I I
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1 __ ANTI EARTHQUAKE-------------- NO PULSE CONTROL--------< .. ~ PULSE CONTROL
FIGURE 6-2. EFFECT OF ANTIEARTHQUAKE PULSE CONTROL ON THIRD FLOOR VELOCITY AND DISPLACE~ffiNT OF UCB TEST STRUCTURE TO RANDOM BASE MOTION INPUT
6-3
>I-
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R-7824-5489
NO PULSE CONTROL "-
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(a)
NO PULSE CONTROL '"
.•••••.•• /ZERO CROSS ING PULSE CONTROL
.. - ............................................... .
10 TI ME, 5
(b)
FIGURE 6-3. RMS VELOCITY RESPONSE OF UCB STRUCTURE HITHOUT PULSE CONTROL AND \HTH PULSE CONTROL SET FOR SPECIFIED THRESHOLD riND ?OR ZERO CROSSI~G
6-4
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R-7824-5489
SECTION 7
DEMONSTRATION TESTS ON A BUILDING
7.1 OBJECTIVES
The objectives of the Demonstration Test were to specify a
pulse train and compare it to the test pulse train achieved.
Originally, a more complete demonstration was planned for the
moment resisting steel frame structure at the University of
California, Berkeley, project (see Appendix) but development
efforts and teething problems were of such magnitude as to
restrict any extensive calibration and demonstration tests.
7.2 DEMONSTRATION CONFIGURATION
A demonstration test was conducted upon a one-story office
building. This building is a wood frame-stucco structure on a
concrete floor slab foundation. Test configuration is illus
trated l.n Figure 7-1, where one gas pulse unit is mounted
against the concrete slab and an accelerometer is mounted on the
roof. This configuration was necessitated by program limi ta-
tion. Normal procedure would be to mount both pulse units on
the roof.
7.3 SPECIFIED PULSE TRAIN
The specified pulse train is presented in Figure 7-2a and
its Fourier transform magnitude in Figure 7-3a. This pulse
train was adapted from pulse trains used to study the ueB steel
frame structure for a modified EI Centro 1940 earthquake
(details in Appendix). Figure 7-3a shows the major portions of
the force content below 7 Hz.
7.4 TESTS
Tests were performed on the demonstration building. The
pulse train measured during this test is plotted in Figure 7-2b
7-1
GAS PULSER
___ ---d
CONCRETE TEST STAND
R-7824-5489
00 r X, ACCELERATION
TRANSDUCER
BUILDING
--14--. FORCE
LOAD CELL
FIGURE 7-1. BUILDING DEMONSTRATION TEST, GAS PULSER IN?UT IS INTO CONCRETE BUILDING SLAB; BUILDING IS WOOD-FRfu~E AND STUCCO CONSTRUCTION
7-2
5000
4000
.a 3000 &
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R-7824-5489
PUL~F-rRAd"
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7 8
(b) Pulse train obtai~ed from test
FIGURE 7-2. SPECIFIED INPUT PULSE TP~DI A~m peLSE TRA.n1 OS'I'.;;.nIED FROX TEST ON DEI·lOl~STR.;;'TION BUILDING
7-3
R-7824-5489
3000 ~A BLOC PULSE-TRAIN
2500
2000
..c
. 1500 UJ u a: 0 u..
1000
FREQUENCY, Hz
(a) Specified input pulse train
3000+-----~----~----~----~----~----~----~----~
~A BLDG PULSE TEST
2500
2000
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. 1500 UJ
u a: 0 u..
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II~ 500
[[I I'~ 0 ~~
0 10 20 30 40 50 60 70 80
FREQUENCY, Hz ~A570
(b) Pulse train obtained from test
FIGURE 7-3. FOURIER MAGNITUDES OF SPECIFIED AND ACTUAL PULSE TRAINS
7-4
R-7824-5489
and its Fourier transform magnitude given in Figure 7-3b.
Motions of the test building are given in Figure 7-4a for accel
eration, in Figure 7 -4b for velocity, and in Figure 7 -4c for
displacement.
7 .5 SYSTE~'I PERFORMAl.'ICE
Examination of the pulse trains in Figure 7-3 show quite
accurate timing of the test pulse train with respect to the
specified pulses. However, deviations occurred with respect to
test thrust amplitudes achieved. These variations are sum
marized in Table 7-1 where the overall impulse was 12 percent
below specified requirements.
Average variation in thrust is 20 percent of specified
excluding the anomaly of the last pulse. Previous analytic
studies have noted that nominal force variations have small
effects upon induced structural motions.
, Investigation of the test pulses was made and plots of t.~e
positions of the metering nozzle are shown in Figure 7-5. Prior
to test, an unpressurized pulse test was performed to verify
correct command signal coding on the computer.' This trace is
compared to the nozzle position trace under transient pressures
of the test. Under pressure, the test position corresponded to
the thrust delivered. Table 7-2 lists the positions and areas
of the nozzle. Addi tional information is provided in Fig
ure 7-6 I covering chamber pressure-time history for the test.
This figure discloses pneumatic surges described in Section 5 on
calibration. It has been concluded that these pressure surges
interact with a balancing piston (Fig. 3-1a) in the plenum cham
ber and affect the servo position control, particularly for the
small to moderate throat areas.
7-5
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R-7824-5489
2 AA SLOG PULSE TEST
a I '
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TI HE, 5
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3
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TIME,s
(b) Velocity-time history (integrated)
2 AA SLOG ·UlSE TEST
-I
-2 0 2 4 5 6 8
TIME,s M573
(c) Displacement-time history (integrated)
FIGURE 7-4. MOTION-TI!1E HISTORIES FROH ROOF OF DEMONSTR.'\TION BUILDING INDUCED BY PULSE TRAI~ (Fig. 7-2)
7-6
R-7824-5489
TABLE 7-1. COMPARISON OF PROGRAMMED AND TEST THRUST AND IMPULSE
Pulse Force Impulse Pulse Duration I No. Program Test Error Program Test Error (sec) ( lbf) (lbf) % (lb-sec) (lb-sec) %
1 0.0948 1230 1250 1.6 116.6 118.5 1.6
2 0.0948 846 1100 30 80.2 104.3 30
3 0.0948 4322 4250 -1. 7 409.7 402.9 -1.7
4 0.076 2742 1850 -33 208.4 140.6 -33
5 0.057 1105 1000 -9.5 63.0 57.0 -9.5
6 0.096 2078 1500 -28 199.5 144.0 -28
7 0.0948 2348 1900 -19 222.6 180.1 -19
8 0.096 3554 3100 -13 341.6 297.6 -13
9 0.095 1400 900 -36 133.0 85.5 -36
10 0.094 302 650 115 28.4 61. 6 115
Total 0.893 1803 1592 -12
TABLE 7-2. METERING NOZZLE, POSITION AND THRUST AREA, FOR NO GAS PRESSURE AND FOR OPERATING PRESSURE
Dry Run Demonstration Test Comparison Pulse No Gas Pressure Operating Pressure
No. Nozzle Throat Nozzle Throat Nozzle ':'hroat position Area position Area position Area
(in. ) (in. 2 ) (in. ) (in. 2 ) % Error % Error
1 0.16 0.63 0.13 0.51 -19 -19
2 0.08 0.35 0.12 0.47 50 34
3 0.65 2.12 0.63 2.09 -3 -1.4
4 0,33 1.22 0.25 0.95 -24 -22
5 0.12 0.48 0.13 0.51 8 6.3
6 0.28 1. 05 0.21 0.82 -25 -22
7 0.37 1.33 0.32 1. 20 -13.5 -9.8
8 0.58 1. 95 0,57 1. 80 -1. 7 -7.7
9 0.18 0.9 0.13 0.51 -28 -43
10 0.038 0,18 0.11 0,45 189 309
7-7
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R-7824-5489
SECTION 8
UTILIZATION
8.1 TECHNICAL PAPERS
In fulfillment of "t..'1.e utilization plan covered by this
grant, five technical papers which resulted from- this research
have been presented at symposiums and conferences. These papers
received peer review and have been published. A sixth paper has
been submitted for publication. Reprints of the following
listed papers are provided in the Appendix of this report.
"Earthquake Environment Simulation by Pulse Generation, II Proc. 7th World Conf. on Earthquake Engineering, Geoscience Aspects, Pt. II, pp 73-80, Istanbul, Turkey, Sep 1980.
"An Optimization Procedure for Pulse-Simulated Response,1I ASCE Nat'l. Conv., Jnl. Struct. Div. ASeE, Sep 1981, pp 1745-1761.
Dj'TI a..'1l i c 107:ST9,
"Development and Use of Force Pulse Train Generators, II ASCE/EMD Specialty Conference, Proceedings on Dynamic Respone of Structures, Experimentation, Observation, Prediction and Control, G. Hart, Ed., Atlanta, Jan 1981.
II Anti-Earthguake Application of Pulse Generators," ASCE/EMD Specialty Conference, Proceedings on Dynamic Response of Structures, Experimentation, Observation, Prediction and Control, G. Hart, ed., Atlanta, Jan 1981.
"Pulse Excitation Techniques, II Society of Automotive Engineers, Aerospace Congress & Exposition, Anaheim, CA, Oct 25-28, 1982, Pub. IIAdvances in Dynamic Analysis and Testing, II SP-529 and the 1982 Transactions of the SAE, Sep 1983.
lIDevelopment of a Pulse Rocket for Earthquake Excitation of Structures,lI submitted for publication.
8.2 DISSEMINATION
Dissemination of this report has been accomplished with
copies sent to t..'1e following academic, professional organlza
tions, government agencies, and privatecorporatons.
8-1
Academic Institutions:
California Institute of Technology California state University, Los Angeles Columbia University Georgia Institute of Technology -Kansas state University Massachusetts Institute of Technology Princeton University Rice University Stanford University
University of California, Berkeley University of California, Irvine
R-7824-S489
University of California, Lawrence Livermore National Laboratory
University of California, Los Angeles University of Illinois University of Michigan University of Minnesota University of Missouri, Rolla University of Nevada, Reno University of Southern California University of Texas
Professional societies: American Technology Council, Affiliated with
structural Engineers Association of California Earthquake Engineering Research Institute
Federal Government organizations:
Dept. of the Army
Corps of Engineers, Huntsville Div. Construction Engineering Research Laboratory Office of the Chief of Engineers waterways Experiment Station Harry Diamond Laboratories
8-2
•
R-7824-5489
Dept. of the Navy
Naval civil Engineering Laboratory (now CEL) Naval Facilities Engineering Command
Naval Research Laboratory
Naval Ship systems Command
Nuclear Regulatory Commission
Tennessee Valley Authority
Veterans Administration
Dept. of Energy, Division of Reactor Design and Development
Dept. of Transportation, FHWA
NASA, Langley
Defense Nuclear Agency Dept. of Defense Explosives Safety Board
Federal Emergency Management Agency
National Technical Information Service
Dept. of the Air Force, Weapons Laboratory
Industrial Organizations
Portland Cement Association Electric Power Research Institute
Southwest Research Institute
state Government Organizations: California Dept. of Transportation California State Office of Architecture and Construc
tion in the Department of General Services
California Legislature Joint Committee on Seismic Safety
California State Building Standards Commission
Private corporations The Aerospace Corporation
Rockwell International
Hughes, Fullerton, CA
Computex, Inc.
8-3
R-7824-5489
SECTION 9
RESULTS
The gas pulse system performed reliably and safely.
Start-up, shut-down and repeat tests may be performed quickly
and efficiently. Repeat tests depend upon charging time of the
high pressure supply tanks. In general, this recharging time
amounted to one hour. Changing pulse train commands involves
entering only time and amplitudes on the keyboard of the control
microcomputer. The system is readily transported to test sites,
and set-up time is expected to be less than a day for two tech
nicians.
Output force at 2640 psig chamber pressure is 9,600 lbf and
minimum pulse width is 26 msec. Delay time from input command
signal to the 50 percent rise time of the pulse is 13 msec.
Each pulse unit has a gas storage capacity of 10.2 ft3 for
134 lbs of gas at 2640 psig. Gas storage units may be connected
to one pulser unit if desired for extended tests. Signal moni
tors provide time-history records of input command signals,
metering nozzle position, chamber pressure and output force.
Design of the gas pulse generator employed conventional
one-dimensional gas flow equations. comparisor:s of calculated
to test results were satisfactory. Programming of pulse trains
is performed at this time from the one-dimensional flow equa
tion. wi th more test runs, calibration curves will be used.
In ~~e early design stages, there was concern about thrust
efficiency due to the potential rise of compression shocks at
the tip of the nozzle in the supersonic diffuser and the effects
of water vapor in the storage gas. In addition, the increase in
the ratio of specific heats with pressure and at low tempera
ture, was expected to reduce thrust. None of the foregoing
effects appears to be significant, at least from the measure
ments and tests made to date.
9-1
Rapid opening 0 f the
oscillation in the plenum
R-7824-5489
metering nozzle induced
chamber and supply hose
pressure
systems.
Pulse duration at or longer than the pneumatic surge period,
reduced nozzle efficiencies by as much as 21 percent. At small
to moderate nozzle openings, these pressure surges acted upon a
balancing piston in the plenum chamber. These surges limited
the ability of the servo control to compensate, with the result
that nozzle openings can fall short of commanded positions up to
25 percent for moderate openings, and to exceed commanded posi
tion for small openings by up to 200 percent.
An algorithm employing adaptive random search was success
fully developed to generate pulse trains which will closely
approximate structural motions induced by earthquakes. This
algorithm permits placement of pulse excitation units in multi
ple locations of test convenience. computer stUdies of several
structures yielded information on the performance required for
pulse units with respect to thrust, pulse widths, and impulse.
A counter-earthquake algorithm was also developed to reduce
structural motions induced by earthquakes. Several computer
studies were made, and demonstration tests using an analog
computer were successfully accomplished. This algorithm is
currently limited to fixed amplitude pulses.
Demonstration tests on a single-story structure were suc
cessful. One pulse unit was fixed to the building concrete base
slab and the induced motion was recorded from a roof accelero
meter. Program restraints and building safety permitted the use
of only one pulse unit, and this unit was attached to the con
crete floor slab of the building. Normally both pulse units
would be placed on the roof and expected building motions would
be at least 3 orders of magnitude greater than was obtained in
the demonstration test. Total test input impulse was 12 percent
below specified due to the pnewnatic surges discussed above.
9-2
R-7824-5489
The research work produced as a result of this grant has
been utilized through the publication of five technical papers.
A sixth paper has been submitted for publication. Distribution
of this report has been made in accordance with the utilization
plan.
9-3
R-7824-5489
SECTION 10
CONCLUSIONS
Two gas pulse generating systems were produced and are in
a state of operational readiness. These systems are suited for
earthquake testing of small buildings, large industrial equip
ment and frame structures such as microwave and power trans
mission towers.
An efficient pulse train algorithm was developed for use in
programming the gas pulse system for motion simulation. A
simple anti-earthquake algorithm was also developed. This
algorithm when used in conjunction with various types of pulse
uni ts shows promise in the reduction of structural motions at
the damage or life threatening thresholds. In its present form,
the anti-earthquake algorithm is limited to preselected fixed
amplitude pulses. Further development work is required to
improve the algorithm.
Additional calibration tests at low to medium nozzle throat
settings are required. These data will permit improvements and
ease in programming pulse trains with respect to the gas supply.
Surge suppressors need to be added to the plenum chambers to
improve nozzle efficiencies and to reduce the interaction of
pneumatic surges with the plenum chamber balancing piston.
10-1
R-7824-5489
REFERE.i'lCES
Bekey, G.A. and Ung, M.T. IIA Comparative Global Search Algorithms, 11 IEEE Trans. Cgbernet, SMC-4:1, 1974, pp 112-116.
Eval ua ti on 0 f Two Sgstems, Man, and
Binder, R.C. Advanced Fluid Dgnamics and Fluid Machinery. New York: Prentice Hall, 1951.
Corvin, P. and steinhilber, H. IIS e isrnic Tests at the HDR ity Using Explosives and Solid Propellant Rockets,lI 6th Int. Conf. on struct. Mech. and Reactor Tech., K14-3, Paris, 1981.
FacilTrans. paper
Ellenwood, F.O.; Kulik, N.; Gray, N.R. Specific Heats of certain Gases Over wide Ranges of Pressures and Temperatures, Cornell Univ. Bull. 30, Oct 1947.
Gurin, L.S. and Rastrigin, L.A. II Convergence Search Met.'1od in the Presence of Noise, 11
Remote Control, 26:9, 1965, pp 1505-1511.
of the Random Automation and
Housner, G. W. "Characteristics of strong-Motion Earthquakes," Bull. Seismol. Soc. Amer., 37:1, Jan 1947, pp 19-27.
Hudson, D. E. "Some Problems in the Application of Spectrum Techniques to strong-Motion Earthquake Analysis, 1/ Bull. Seismol. Soc. Amer., 52:2, Apr 1962, pp 417-430.
Jeans, J. Kinetic Theory of Gases. New York: Dover.
Masri, S.F.; Bekey, G.A.; and Safford, F.B. tlOptirnum Response Simulation of Mul tidegree Systems by Pulse Excitation, 1/
Jnl. DTjIl. STjstems, l1easurement and Control, ASl'JE, 97: 1, Nar 1975.
"An Adaptive Random Search Method for Identification of Large-Scale Nonlinear Systems, 1/ 4th Symp. for Identification and System Parameter Estimation, Int. Federation of Automatic Control, Tbilisi, USSR, Sep 1976.
"A Global Optimization Algorithm Using Adaptive Random Search," Applied Mathematics and Computation, 7, 1980, pp 353-375.
Masri, S.F. and Safford, F.B. "Dynamic Environment Simulation by Pulse Tec.b~'1iques, 1/ Froe. ASCE Eng. Neeh. Div., 101: EI1I I Feb 1976, pp 151, 170.
Rastrigin, L.A. "The Convergence of the· Random Search r'Iethod in the Extremal Control of a Many Parameter System,l/ Automation and Remote Control, 24:11, 1963, pp 1337-1342.
R-1
R-7824-5489
Safford, F.B. and Masri, S.F. "Analytical and Experimental Studies of a Mechanical Pulse Generator," Jnl. Eng. for Industry Trans., ASME, Series B., 96:2, May 1974.
Sato, Y. and Sawabe, Y. "vibration Tests on Reinforced concrete Towers for Microwave Telecommunication," Proc. 7th World Conf. on Earthquake Eng., Istanbul, Turkey, Sep 1980.
Schumer, M.A. and Steiglitz, K. "Adaptive Search," IEEE Trans. Automatic Control, 270-276.
step Size Random AC-13:3, 1968, pp
Scruton, C. and Harding, D.A. Measurement of structural Damping of a Reinforced Concrete Chimneg Stack at Ferrghridge "B" Power Station, NPLjAEROj323, Wallingsford, England, 1957.
Seifert, H.S. and Brown, K. Ballistic Missile and Space Vehicle Sgstems. New York: JQhn Wiley and Sons, 1961.
sutton, G.P. Rocket Propulsion Elements. New York: John Wiley and Sons, 1956.
Zucrow, M.J. Aircraft and Missile Propulsion, 2 Vols. New York: John Wiley and Sons, 1964.
R-2
R-7824-5489
APPENDIX
. PAPERS PUBLISHED AS A DIRECT RESULT OF THIS RESEARCH GRANT
• Optimization Procedure for Pulse-Simulated Response
Earthquake Environment Simulation by Pulse Generators
• Development and Use of Force' Pulse Train Generators
• Anti-earthquake Applications of Pulse Generators
Pulse Excitation Techniques
A-I
Pages A-2 through A-21 have been removed.
Due to copyright restrictions, the paper, "Optimizat~on Procedure for Pulse-Simulated Response," by Sami F. Masri and Frederick 8. Safford, has been omitted.
Journal of the Structural Division, l1.SCE, Vo1. 107, No. 5T9, Proc. Paper 16521, September 1981, pp. 1743-1761.
r- I -.'-'
NSF Grant CEE-7715010
PROCEEDINGS OF THE SEVENTH WORLD CONFERENCE ON' EARTHQUAKE ENGINEERING
Sep~ember 8~ 13,1980 Istanbul, Turkey
GEOSCIENCE ASPECTS, PART II o
STRONG MOTION INSTRUMENTATION AND DATA COLLECfION
INFLUENCE OF LOCAL CONDITIONS ON GROUND MOTION
SIMULATED AND ARTIFICIALLY GENERATED GROUND MOTIONS
SPECTRAL ANALYSIS AND INTERPRETATION OF GROUND MOTION
A-22
EAR'!EQUA,KE ENVIRONMENT SIMlJLAIION BY l?ut.SE GENERATORS
by
S.F. MasriI and F.B. SaffordII
. SUMMARY
Simple mechanical pulse-generating devices of fairly recent development are capable of producing short duration forces of large magnitudes over a wide frequency range that can be controlled to satisfy multimode system response. This paper is concerned with the simulation of the motion of typical structural systems subjected to earthquake environments by using suitable pulse trains applied at various locations on the structure. The pulses are selected in such a way that the reSUlting vibration of the structure matches closely the response that would be produced by the earthquake excitation, as deter.nined by an appropr{ate error criterion. A suitable optimization algorithm is presented and applied to twO realistic example structural systems. It is shown that pulse-excitation techniques offer a viable alternative to conventional testing approaches.
INTRODUCTION
The capability for simulating the response of structures to transient dynamic loadings, such as earthquakes and blast loads, is useful for testing structural adequacy, for improving mathematical models, and for investigating the response of equipment in a structure [1}. In addition to various types of vibration generators that are appropriate for certain classes of structural systems, large testing facilities (which have limited availability) and ground-explosion approaches (vhich are economically prohibitive) can be used for dynamic tests on equipment and structural systems (2,31.
Hausner [4} demonstrated the feasibility of using a sequence of discrete pulses vith random a~plitude to represent the effects of earthquakes on dynamiC systems. Scruton and Harding [5] used a crude explosive c~arge to excite a tall chimney in order to determine its damping characteristics.
A simple mechanical pulse-generatin~ device of fairly recent development (6] is capable of producing short duration forces of large magnitudes over a wide frequency range that can ~ controlled to satisfy multimode system response. Such force pulse generators have been successfully used to simulate the in-place motions of up to 500 Hz in equipment ~eighing up to 200,000 Ib and in also measuring system impedance functions [7,8).
I Professor, Civil Engineering Deparcnent, University of Southern California, Los Angeles, CA 90007, U.S.A.
Ilprincipal Engineer, Agbabian Associates, 21 Segundo, CA 90245, U.S.A.
73
A-23
This paper is concerned with the simulation of the motion of typical structural systems subjected to earthquake environments, by using suitable pulse trains applied at various locations on the structure. Since a discrete number of pulses superficially presents an appearance quite different from a continuous earthquake ground motion, it becomes necessary to select the pulses on the structure in such a way that the resulting vibration matches as closely as possible the response produced by the earthquake ground m~tion as determined by an appropriate error criterion.
OPTIMIZATION TECHNIQUE
Statement of the Problem
Note that the method of Fig. 1 reqUires that the criterion response co the continuous input be known, which would generally not be true in practice. To accomplish this objective, the approach proposed here assumes that: '(1) a mathematical madel of the system under study is known and (2) the 'inputs of interest (e.g., earthquake or nuclear blast) are given. Under these conditions, the "criterion response" can be calculated and subsequently used to obtain the pulse trains for the simulated test.
The basic criterion used in this study is the integral squared error between the reference and simulated response, evaluated at a sufficient number of locations within the mUltiple degree-of-freedom system to characterize it as completely as possible. Given the error criterion, then the pulse occurrence times, pulse widths, and the pulse' amplitUdes are selected by a systematic search algorithm such that the error is minimized.
(e.) PUI$oI test on. tlTlK1ur.
FIGURE l. PROCEDURE FOR PULSE S IMUUTlONI rr5T OF A STRUCruRE TO S IMUUrr EAATOOUAK£ RESPONSE
74
A-24
fiGURE 2. AOAPTlvt RANDOM SEARCH, WIDE RMiG£ AND PRECISION STEP SIZE
Formulation
Consider an n-degree-Qf-freedom system governed by m nonlinear firstorder differential equations of the form
i .. 1,2, •.• ,m (1)
where m" 2n, and the system is subjected to an excitation force vector ~(t). Let the res~onse of the system to this force (the criterion response) at location i in the structure be denoted xi(t), i = 1,2, ••• ,k, where k is the number of locations whose motion is to be monitored.
In order to compare the response of the system model, ~(t), to the criterion response x(t), we select the displacements and velocities at k locations. We now define a nonnegative error criterion
J (2)
which measures the "goodness of fit" of the system response variables :5-(t) to the snecified response x(t). The k constants C1 and C2 are ... l.i weighting factors that can be adjusted to emphasize or de~~?has~z~ the significance of the fit at different points in a structure, since a good fit at some points may be much more important for simulating damage and malfunctions.
_ The specified or criterion responses ii(t) are those recorded in the structure (as during an earthquake) or obtained from applying~nown excitation forces to the model of Eq. 1. Since our objective is to find a pulse excitation F(t) that produces a response x(t) as close as possible co g(e), we r~;trict each component of fCc) -co the form
where
and
Amplitude of the j th 'pulse
Width of the j£h pulse
Initiation time of the J!h pulse
u(t) Unit step function
The problem may now be stated precisely as follows:
(J)
Given a system that is described by Eq. 1 and a desired time history vector ~(c), find the set of numbers {t j , Aj • Wj }, j ~ 1.2 •... ~, ~hich describes each component of the excitation vector such that the error criterion of Eq. 2 is minimized.
75
.21.-25
Algorithm
The optimization problem consists of selecting the triplet of numb",." (ti' Aj , W'j)' which characterizes each input pulse at various systl'm ">:I'i tation points. In principle, a large number of optimization procedurl's I", such problems are available [9]. However. in view 0: the large nllmi", r "I
parameters possible in this system, the set of feasible optimization pr,,.., dures is quite limited. Consequently, an adaptive random search algor i LI,[n
[10] was selected to determine the optimum parameter values for the puis.' trains.
The algorithm for the adaptive random search consists of alternatiof. sequences of a global random search with a fixed value for the step-size variance 0 2 followed by searches for the locally optimal 0 2 . Fig, 2 illustrates the adaptive algorithm whereby a very wide-range search selecls the best standard deviation of step size 0 for the coarseness of the increments used, followed by a sequential precision search of finer increments. As the rate of convergence decreases, a new preCision search is made, but is directed toward a smaller step size. At selected iteration intervals, the wide-range search is reintroduced to prevent convergence to ,
.. local minima. The complete algorithm is described in [101,
APPLICATIONS
The optimization procedure was then applied to two test structures: (1) a typical 25-story building model and (2) a 3-story building frame model that has been extensively tested at the University of California at Berkeley (UCB) shaking table facilities. In each case, the mathematical models of the structures were subjected to a ground motion corresponding to El Centro earthquake record to generate the criteria response. Then for each structure, an appropriate selection of pulse trains was determined in order to minimize the mean-square deviation between the criterion response and the simulated response. The pulse characteristics are, at the same tim<-, constrained to realizable physical values for the test.
Model of 25-Storv Building
The system shown in Fig. 3 is a 25-story office building designed in accordance with applicable building code provisions for recommended lateral force requirements [11]. Modal analysis of this building, treated as a linear elastic structure, yields the mode shapes and natural frequencies'shown in Fig. 4.
nro "' il1U ,"
n ~rYr,M! II
IJ
!UlllllH<;
. 107 • : rn2f1l
MOO! , 1 j
PUlIOO. I 1.91 D.1'Il D. ';) 0.'1 D. ~
FIGURE 3. GAS PUlSERS ARRAYED f{)R FIGURE 4. BUILDING NATURAL MODES EART~UAKE S IMULAT ION Of VI BRATJON TEST Cf A MULT ISTORY BUILDING
76
A-26
To illustrate the simulation procedure outlined above. it was decided to use four pulse-excitation locations at modal antinodes (Floors a, 13, 18, and 23) and to attempt to match the response of two locations (Floors 13 and 23). Due to the linearity of the system, its transient response to pulse trains could be determined by using the convolution integral approach. The necessary impulse response functions were determined and are illustrated in Fig. 5 where hi (j) (t) denotes the response of location i due to a unit impulse applied at location j.
The El Centro 1940 earthquake ground motion was used as specified base input, and it is resulted in the criteria response snown in Figs. 6a and 6b as solid lines. The earthquake criteria response was simulated by four suitable pulse trains using the optimization algorithim outlined above. The simulated response is superposed on top of the criteria
&,7, ';.
,/II , .
; , ,,"
FIGURE 5. IMPULSIVE OISPlACEME~ RESPO~SE TO 2S 00f SYSTEM
INOO: ~ESi'ONSE P'JI.SES 'lOCO
CD G) response in Fig. 6, and the time histories of the four required pulse trains are shown in Fig. 7. The ordinates of the response and excitation time histories shown in Figs. 6 and 7 are expressed in terms of dimensionless units.
ffif~ _ ~I~'
--C~IT'ElI'ON
""~~ i~ !
It is clear from the comparison shown in Fig. 6 that a good match is obtained bet~een the criterion and simulated response. Note that this simulation of the motion over a period of =20 sec required =13 pulses in each of the four pulse trains.
-- SIMULU'[Q
»'»""h»",
,a)
TlMf ~
0.)
" ~ ~
!hI
~) a 11ME ~
-:::~~1 TI~ ~ FZ 0
-), !a' ), la'~rIMf ~
FJ 0
-), la'
"l/~TlMf ~ F4 a ,
.J , !t? o TIME ~
fIG~RE 6. CCMPARISON Of CR IITR ION AND SIMULATtD RESPONSE OF fiGURE 7. OPTIMUM PIJLSE r'~I~\ Z5 OOf SYSTU~ FOR 25 00f sysrE!~
77
A-27
Model of UCB Frame
. The test structure shown in Fig. 8 has been extensively investigated, both experimentally 112) and analytically {13J at the University of California, Berkeley. In the present study, the computer program SAP6 [14} ~a5 used to determine the mode shapes and frequencies of a linear model of this structure, and these dynamic characteristics are shown in Fig. 9.
u. n7.) "'
'I 1
• ;
• L
FRONT ruvATION
~ .. S"'.
~ 1'''''''-;1 I" 'I"~ Il i~ "
Mlllj '" . . .. ~. . . . ..
i[XJ~ 1 'l I, I~
fJ., .. jl SID!' £\!VAllO"
FIGURE &. UCS TEST STRUCTURE 1\31
fi' 'R';H l ;. .: I
; Ii:: ;
: ;:; ~ v:
. . I !: : 2.D HI 1.'15 HI U.S HI
Fl······_·· .. ·· Fl·' .... R .......... .... .... .._.: I ~-----.. -. .-.. ..
: :
«l.OH:
FIGURE 9. MODE SHAPES OF UC8 FRAME OEiEilf,\\NEO SY S ... ?~
Pulse trains ~ere to be applied at the three floor locations. The needed impulsive response functions ~ere analytically determined and are shown in Fig. 10. The criteria response to El Centro 1940 earthquake ~as like~ise analytically determined by using SAP6, and the results are shown as solid lines in response time history of Fig. 11. The adaptive random research optimization procedure ~as again used to determine the required pulse trains. The resulting simulated motion and the three reqUired pulse trains are shown in Figs. 11 and 12.
This example again results in excellent agreement between the criterion and simulated response. In addition, the response spectra of various locations satisfactorily matched the criterion spectra at corresponding locations.
CONCLUSIONS
On the basis of the investigation reported herein, it is concluded that pulse-excitation techniques offer a viable alternative to large testing facilities (which have limited availability) and ground-explosion approaches (~hich are economically prohibitive) in simulating earthquake effects on structures, particularly ~hen rnultiaxis excitation capability is needed.
ACKNOWLEDGMENT
This study ~as supported by the United States National Science Foundation under Grant No. PFR77-1S010. The assistance and guidance provided by Dr. John B. Scalzi is greatly !ppreciated.
78
A-28
4
'-r } tttttt~ H+!i fl+tffiiittfu'tJ+t++\+\t+t
. ~
-4 0~--r-IM£---1-., -4~0 --r-'M£---U
TIME 1. S
~ 'I ~'
-4:-0 --r-'M-E--1-.5
-1 x ~~ ~ 0'1 I l~.l~'''!!''n' F _ -h =5 \I H~rnn 1M .. i' .
~.J Q'---rl-ME--I-.5
FIGURE 10. IMPULSE FUNCTIONS FOR UCB fRMlE
3 11 3 I la'
: ~ 1 i. 111~~~1~ F1-! Fl FZ-n-
-CR~~O: !llfllllllllllltl!lilllll' ~
-3 I 10' ---SIMUL-.rEO '30 TIME L5 a TIME lS 1 I IO!!
I I '2 ~ ,llllllllilll!IIIIIl!II',1 F2 z
~o 'liimmi~jIT"IWW-'"
-J a :1 I 10' TIME L5 a TIME
J I la' , ~ n z
~o ,
.. -3 a .J I 10'
TIME lS 0 TlI,IE IS
FIGURE 11. CCMP~RISO~ Of CRIIT.RION AND SIMUUlITn f ICURE 12. OPTIMUM PULSE T'lAINS fOR ilC8 fRA.\\£ RESPO~SE ~ UC3 FR '.\'.E
79
A-29
I.
I.
4.
5.
n.
7.
R.
9.
10.
II.
12.
13.
14.
REFERENCES
Rousner, C.W. "Earthquake Environment Testing," Proe:. of it Workshop on Simulation of Earthquake Effects on Structures, San FranciRco, Sept. 7-9, 1971. Washington, DC: National Academy of Engineering, 1974.
Rudson, D.E. "Dynamic Tests of Full-Scale Structures," .!::2c. Dvnamic Response of Structures, Instrumentation, Testing Methods, and System Identification. Univ. of Calif. Los Angeles, Mar 30-31, 1976.
Bouwkamp. J .C. "Dynamics of Full-Scale Structures," in Applied Mechanics in Earthouake Engineering, New York: ASME, 1974.
Rousner, C.G. "Characteristics of Strong-Motion Earthquakes," Bull. Seis,"o1. of Amer., 37:1, Jan 1947, pp. 19-27.
Scruton, C. and Harding, D.A. Measurement of the Structural Damping of a Reinforced Concrete Chimney Stack at Ferrybridge "B" Po ... er Station. Wallingsford, England: NPL/Aero/32J, 1957.
Safford, F.B. and Masri, S.F. "Analytical and Experimental Studies of a Mechanical Pulse Generacor," J. of Engineering for Industrv, ASME, Series B, 96:2, May 1974, pp. 459-470.
Safford. F .B. et a1. "Air-Blast and Ground-Shock Simulation Testing of Massive Equipment by Pulse Tee:hniques." 5th Int. Svmp. on Militarv Application of Slast Simulation. Fortifikationsforvaltningen, Stockholm. S ... eden, May 23-26, 1977.
Yates, D.G. and Safford, F. B. "Measurement of Dynamic Structural Characteristics of Massive Builrlings by Righ-Level Multiple Techniques," Shock & Vibration Bull., 50, SVIC. Washington, DC: Naval Res. Lab, 1980.
Rimmelblau, David M. Applied Nonlinear Programming: New York: McGraw-Hill, 1972.
Masri, S.F.; Bekey, G.A.; and Safford. F.B. "An' Adaptive Random Searcl .. Method for Identification of Large-Scale Nonlinear Systems," 4th Svmp. for Identification and System Parameter Estimation, Int. Federation of Automatic Control, Tbilisi, USSR, Sep 1976.
Blume. J.A.; Newmark, N.M.; and Corning, L.R. Design of Multistorv Reinforced Concrete Buildings for Earthquake Motions. Skokie, IL: Portland Cement Association, 1961.
Clough, R.W. and Tang, D.T. Earthquake Simulator Study of a Steel Frane Structure, Experimental Results, Vol. I, EERC 75-6. Berkeley, GA: Vaiv. of Calif. Earthquake Engineering Center. 1975.
Tang. D.T. Earthouake Simulator Study of ~ Steel Fr~e Structure, Analvtical Results. Vol. 2, EERC 75-36. Berkeley. GA: ('niv. of Calif. Earthquake Engineering Center, 1975. -
SAP 6 Comt>uter Pro~ra", Manual. Civil Eng. D<>pt., U..,iv. of Southern California, 1978.
80
A-30
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onic
Il
loti
on
s to
ex
pecte
d
mu
lti
freq
uen
cy
resp
on
se-t
ime
his
tory
m
oti
on
s.
The
d
evel
op
lOen
t o
f fo
rce
pu
lse
train
g
en
era
tors
ex
hib
its
clH
lsid
erd
lde
pro
llli
se
to
mee
t th
e
fore
go
ing
fo
r th
e
stu
dy
o
f li
near
and
n
on
lin
ear
dyna
mic
re
spo
nse
s o
f la
rge
str
uctu
res.
I NT
IWIl
lIC
T I
(IN
------------
---
I R
ecen
t an
aly
tical
aud
ex
peri
men
tal
stu
die
s!l
] in
dic
ate
th
at
a ru
di-
0'>
Ille
llt,
ay
seri
es
of
recta
ng
ula
r o
r o
ther
sim
ple
p
uls
es
cou
ld
be
con
vo
lved
N
w
i th
lh
e
imjl
ub
e fu
ncti
on~
of
a str
uctu
re
to
ind
uce
m
oti
on
s clo
sely
d
pp
rux
illl
dti
llg
th
ose
ca
use
d
by
natu
ral
and
man
-mad
e ~vents.
Th
is
resu
lt
gre
atl
y
sill
ll'J
ifie
d
the
co
ntr
ol
of
hig
h
ener
gy
d
ev
ices
as
the
pro
ble
m is
re
du
ced
to
th
ree
fun
cti
on
s o
f o
n, ~ff,
and
amp
litu
de
co
ntr
ol.
It
was
tu
rlil
ec
det
erm
ined
th
at
the
"x
cit
ati
on
co
uld
als
o
be
pla
ced
d
irectl
y
on
strU
Ltu
res
at
one
locati
oll
o
r at
mU
ltip
le
locati
on
s o
f te
st
con
ven
ien
ce
dlld
il
l si
llg
le
or
Ulu
ltip
l'e
ax
es.
W
hen
the
str
uctu
ral
ex
cit
ati
on
is
ca
use
d
by
bas
e m
oti
on
, p
uls
e
sim
ula
tio
n w
ith
g
en
era
tors
att
ach
ed
to
th
e ,d
me
.tcu
ctu
re
cari
d
up
licate
th
e n
atu
ral
or
man
-mad
e ev
en
t w
ith
th
e ex
c"p
liu
ll
of
the
rig
id
body
m
od
es.
Sev
er"
l la
rge
ener
gy
d
ev
ices
lIIay
be
ad
apte
d
for
pu
lse
train
ex
ci
tdti
OIl
. T
hes
e in
clu
de
po
int
sou
rce explosive~,
chem
ical
ro
ck
ets
, m
etal
cu
ttil
lg,
and
reacta
nce
by
gas,
w
ate
r,
or
pro
jecli
les.
The
d
evel
op
men
t al
ld
dl'
l'ii
catl
oll
s o
f se
vera
l m
etal
cu
ttin
g
syst
elJl
s are
d
iscu
ssed
to
geth
er
wi
til
" In
llse
m
od
ula
ted
g
as
rea
cta
nce
sy!:
item
.
Inte
re.t
ill
g o
b.e
rvati
oll
s ca
n
be
mad
e th
rou
gh
ex
peri
men
ts
and
ex
ami
lIat
ion
s u
f p
uU
,e
train
. il
l b
oth
th
e
tim
e an
d
freq
uen
cy
do
mai
ns.
A
si
llg
le
iJll
ise
is
dis
pla
yed
in
F
igu
re
1 fo
r b
oth
d
om
ain
s.
Ho
wev
er,
a
IA.s
ucia
te,
Agb
abid
fl
Ass
ocia
tes,
E
l S
egu
nd
O,
Cali
forn
ia
9024
5 ~l
'rof
"ss(
)r,
Sch
oo
l o
f E
ng
ille
eri
ng
, U
niv
ers
ity
o
f S
ou
ther
n C
ali
forn
ia,
Los
A
ng
el""
C
ali
fon
lia
90
00
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72
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RC
E
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LSE
TR
AIN
GE
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RA
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RS
73
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RE
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fRE
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lse
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ry
MU
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E HI
STOR
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ve
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) P
uls
e parameter~
a -1
-2 a
20
~o
60
80
500
TIM
E,
ms
(d)
Pu
lse
train
(a
dap
tiv
e)
GENE
RATI
ON
OF P
ULSE
TR
AIN
TO
MAT
CH
CRIT
ERIO
N
FREQ
UENC
Y SP
ECTR
UM,
ADAP
TIVE
RA
NDOM
SEA
RCH
7.J
DY
NA
MIC
RE
SP
ON
SE
OF
ST
RU
CT
UR
ES
co
llecti
on
o
f si
x
pu
lses
all
o
f id
en
tical
am
pli
tud
es
and
d
ura
tio
ns
bu
t sp
aced
at
dif
fere
nt
inte
rvals
g
en
era
tes
a co
nsi
dera
bly
d
iffe
ren
t sp
ec
lfll
lll,
as
sh
own
in
Fig
ure
2
. A
llo
win
g
pu
lse
am
pli
tud
es,
p
uls
e d
ura
tio
ns,
an
d p
uls
e
spacin
gs
to
be
vari
ab
le
para
mete
rs
perm
its
co
nsi
dera
ble
le
eway
in
sh
apIn
g
the
freq
uen
cy
sp
ectr
wn
. F
igu
re
3 il
lustr
ate
s
a m
eth
od
o
f se
lecti
ng
a
pu
lse
train
to
p
rod
uce
a
cri
teri
on
spe~trum
wh
ere
the
para
m
eter
s o
f am
pli
tud
e,
pu
lse
wid
th,
and
p
uls
e
spacin
gs
are
sp
eC
ifie
d
by
all
it
era
tiv
e
op
tim
izati
on
al
go
ritl
llll
(Z}
. A
dd
itio
nal
flex
ibil
ity
ca
n
be
acll
iev
ed
by
perm
itti
ng
lh
e
pu
lse
shap
es
to
be
such
as
h
alf
-sin
e,
saW
to
ulh
. o
r ex
po
nen
tial
and
in
v
ari
ou
s co
mb
inati
on
s.
MO
TIO
N
SH
fUl.
AT
ION
O
F ST
HU
CTU
HES
--
--~ ~-----------------
l.ar
ge
and
m
assi
ve
str
uctu
res
and
eq
uip
men
ts
are
la
rgely
su
bje
cte
d
lo
(I)
bas
e m
oti
on
ex
cit
ati
on
as
fr
om
eart
hq
uak
es
and
fr
om
g
rou
nd
sh
ock
s in
,lll
(cd
by
co
nv
en
tio
nal
ex
plo
siv
es
or
nu
cle
ar
wea
po
ns
and
(2
) d
istr
ibu
te
d
dir
1
0d
ds
as
frol
O
lorn
ad
oe",
h
igh
w
ind
s,
and
w
eapo
n b
lasts
. W
here
ti
le
resp
on
se
of
these
sy
stem
s is
p
red
icte
d
and
th~
dyna
miC
ch
ara
cte
ris
llC
G
arc
kn
own
by
an
aly
sis
or
test
(mod
e sh
ap
es,
d
amp
ing
, an
d
tran
sfe
r fu
ncti
on
s),
tests
o
f th
ese
sy
stem
s re
qu
ire
an
inv
ers
e
solu
tio
n
to d
ete
rm
ine
ex
cit
ati
on
fu
ncti
on
s.
Fo
r th
e
bas
e m
oti
on
p
rob
lem
, te
st
ex
cit
ati
on
lI
lust
be
d
cten
llil
led
fo
r o
ne
or
mor
e lo
cati
on
s o
f co
nv
en
ien
ce
upon
th
e
sLru
clu
re;
for
dis
trib
ute
d air
lo
ad
s,
a fe
w
eq
uiv
ale
nt
po
int
locati
on
s o
t co
nv
enie
nce
m
ust
b
e fo
un
d.
It
is
req
uir
ed
th
at
an
iden
tical
resp
on
se
(wit
hin
an
accep
tab
le err
or)
to
th
e
pre
dic
ted
re
spo
nse
(c
rite
rio
n)
cdu
sed
by
n
alu
ral
or
man
-lil
ade
haz,n
ds
be
ob
tain
ed
. T
hes
e 'I
t;W
ex
cit
ati
on
~
fUll
etiD
IlS
ca
n
usu
all
y
be
tou
nd
; h
ow
ever
, th
e
en
erg
y
and
w
avef
orm
s I
re<
juir
.,,1
o
ften
m
dke
testi
ng
im
pra
cti
cal
du
e to
th
e
lim
itati
on
s
of
con
W
v
cnL
ioll
dl
shak
ers
an
d/o
r C
Oti
ts.
W
The
cen
tral
issu
e
in
tesli
ng
is
to
in
du
ce m
ult
iax
ial
mo
tio
n-t
ime
Ilis
tori
"s
on
a str
uctu
re
com
par
able
to
th
ose
cau
sed
b
y
natu
ral
or
man
Ili
dde
hazard
s,
sin
ce
fail
ure
s
and
m
alf
un
cti
on
s are
essen
tiall
y n
on
lin
ear.
fo
rce
pu
lse
train
s
pro
vid
e
pra
cti
cal
met
ho
ds
in m
any
ap
pli
cati
on
s to
tc
st
str
uctu
res
an
deq
uip
men
ts
to
the
thre
sho
lds
of
dam
age
and
mal
fun
cti
on
by
in
du
cin
g
reali
sti
c
resp
on
se
wav
e fo
rrll
s.
Co
mp
ut3
tio
nal
m
eth
od
s to
d
evel
op
th
e
req
Uir
ed
pu
lse
train
s
are
il
lustr
ate
d
in F
igu
res
4 an
d
5 w
ith
dn
d
l'l'
licati
on
to
a
Ilu
cle
ar
po
wer
co
nta
fnm
ent
str
uctu
re
show
n in
F
igll
re
6.
The
co
mp
uta
lio
nal
met
ho
ds
are
it
era
tiv
e
to
ob
tain
th
e
pu
lse
tr,l
lll.
dn
d th
e
pro
ced
ure
ul
ay
be
use
d
for
eit
her
lin
ear(
3]
or
no
nli
near
~ystems[4].
Var
iou
s it
erd
tio
n
met
ho
ds
may
be
u
sed
; th
e
op
tim
izati
on
d
lgtl
rill
llll
(2]
of
Fig
ure
5
usi
ng
a
sph
eri
cal
rand
om
searc
h
wit
h
a p
art
iall
y
dlll
uUld
llC
cO
lltr
ol
af
the
v"r
ian
Ce
has
p
rov
ed
to
be
(Iu
ite
eff
icie
nt.
It
II"
,::).
bee
n
fuu
nd
th
aL
th
e
vd
riil
Hce
ca
n
ran
ge
ov
er
tell
o
rder
ti
of
Ina
gll
ilu
de
l 'W
hll'
il p
erm
lts
rap
id
co
nv
erg
en
ce
and
a
vo
id;J
oce
o
f lo
cLil
m
ild
ma
.
. ~l'l'l.ICATI()NS
A 2
S-s
t6ry
b
uil
di1
l8
(Fig
. 7
),
mo
del
ed
as
d li
near
syst
em
. h
as
the
"""I
e :;
/'dl"
'S
ot
Fi
gu
re
8,
and
u
nd
er
bas
e ex
ci
tati
on
by
th
e
El
Cen
lro
E
arth
qu
ake
YIe
lds
the
mo
tio
n
lim
c h
isto
ries
plo
Lte
d
in
Fig
ure
11
fo
r lh
e 1
3lh
al
ld
23r<
l floors[~J.
Fig
ure
]O
sho\
ols
the d
riv
ing
p
oin
t il
ilP
uls
e tU
llct
ion
s fo
r F
loo
rs
8,
Ll,
U
l.
and
23
as
wel
l as
th
e
tran
sfe
r il
llp
uls
e tU
Il(
liu
lls
bet
wee
n
flo
ors
a'1
<j
each
ex
cit
ati
on
lo
cati
on
. lI
sin
g
the
pro
ce
dil
ies
of
Fig
lJ!"
es
4,
5.
all,1
6
, th
e
forc
e
pu
lse
train
s
of
Fig
ure
9
wer
e
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EAR
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STEM
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dev
el0
l'ed
jo
r 1
'"1
s"
locati
on
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on
F
loo
rs
8,
1:1,
1
6,
ill I
II
23
. T
he
resp
on
se
IJlo
t iu
ns
lnd
uced
b
y
these
p
uls
ers
are
p
lott
ed
o
n
fig
ure
11
an
d
are
v
lrll
lall
y
iden
tical
to
the
mo
tio
ns
cau
sed
b
y
the
El
Cen
tro
E
art
hq
uak
e.
Averd~e
turc
e
req
uir
ed
is
5
0,0
00
ll
lf
and
th
e
av
era
ge
imp
uls
e
is
1/
lid
-se
C.
Fq
;t1
r"s
12
tllr
otl
gh
15
il
lustr
ate
th
e
ap
pli
cati
on
o
f p
uls
e
trll
ins
lo
Illd
uce
a
tra
llsi
en
t siu
e
wa
ve
resp
on
se.
Olh
er m
oti
on
s m
ay
als
o
be
gC
'Jt'
fdl
cd
, su
ch
as
ran
,\u
m
and
ra
pid
sin
e
swee
ps
(ch
irp
).
Th
ese
m
oti
on
s are
u
Lcju
l fo
r m
easu
rem
en
t o
f tr
an
sfe
r fu
ncti
on
s an
d
for
ex
tracti
on
o
f 1I
I0,k
sh
dl'
es.
T
he
str
uctu
re
of
Fig
ure
1
2,
locate
d at
the
Un
ivers
ity
o
f C
ali
/or"
ia,
Berk
ele
y,
hu
a h
een
ex
ten
siv
ely
an
aly
zed
an
d
teste
d
on
th
e
Berk
ele
y
shak
e
tab
lc[6
).
Th
is
str
uctu
re w
ill
be
emp
loy
ed
for
pu
lse
traiu
stu
die
s
to
sim
ula
te
eart
hq
uak
e
mo
tio
ns(
7J
and
to
su
pp
ress
eart
h
'lu
ake
Illo
tio
ns(
6].
In
th
e
latt
er
case
, th
e
Berk
ele
y
shak
e
tah
le w
ill
be
use
d
to
sill
lula
te
eart
hq
uak
e
mo
tio
n
wh
ile
pu
lse
gen
era
tors
w
ill
sim
ult
.IIl
eo
llsl
y
be
us<
',\
to
r",[
uce
t.he
re
su
ltan
t str
uctu
ral
1II
0ti
on
s.
PU
I.S
E
GE
NE
HA
TI N
G [lE
V r C
ES
-
---.
---._
----
----
----
----
--
PlI
lse
gen
era
tin
g
dev
ices
dev
elo
ped
an
d
now
in
d
evel
op
llle
nt
are
C
OII
Il'o
sed
of
a cla
ss
of
mela
l cu
ttin
g
syst
em
s an
d
a cla
ss
of
gas
reac
tdll
ce
sysl
em
s.
Th
e lI
Ieta
l cu
ttin
g
dev
ices
mak
e u
se,o
f th
e
very
h
igh
fo
rces
re'l
'lir
ed
to
cu
t m
etll
l an
d
are
co
nfi
gu
red
sim
ilar
to
bro
ach
ing
to
ols
('!}
. T
he
shap
e
of
a m
eta
l p
roje
cti
on
co
ntr
ols
p
uls
e
wav
e fo
rm
(s'j
Uil
Ce,
h
.. lt
-sin
e,
etc
.).
Th
e v
elo
cit
y
of
the
cu
ttin
g
too
l an
d
lhe
len
gth
o
f tl
te
",eta
l p
roje
cti
on
g
ov
ern
th
e p
uls
e
du
rati
on
[l}
. F
or
the
:v m
ela
l ['
''''l
Ove
d,
cU
ltin
g co
eff
icie
nts
ty
pic
all
y
ran
ge
frol
ll
15
0,0
00
Ib
f/in
3
I jo
r al
um
inu
m
to
30
0,0
00
Ib
f/in
3 fo
r ste
el.
H
etd
l p
ub
e
gen
era
tors
p
ro
~ d
ucin
g
up
la
1,0
00
,00
0
lbf
hav
e b
een
p
rop
ose
d.
Sev
era
l v
ari
eti
es
of
mcld
l cu
tlil
lS
pli
ise
gen
era
tors
are
sh
ow
n
in
Fig
ure
s 16
th
rou
gh
19
au
d
I'lc
ture
d
in
Fig
ure
s 21
th
rou
gh
2
4.
Th
e l'
rog
rall
""ab
le
gdS
p
uls
e
gen
era
tor
sho
wn
in
F
igu
re
20
is
cU
[['c
utl
y
un
der
co
nstr
ucli
on
i te
st
stan
d
cali
bra
tio
lls
wil
l C
O'll
lllen
Ce
in
tlte
fa
ll
of
191\
0.
Init
ial
use
p
rov
ides
for
co
ld
gas
hu
t th
e
syst
em
is
,"
\.I\
,l31
>1"
fo
r b
oth
st
eam
d
nd
ch
em
icall
y
gen
era
ted
h
ot
gas.
T
hru
st
a"l
l'll
lud
es
are
co
ntr
oll
ed
in
th
e
on
-sta
te
by
positionil'l~
the
mete
rin
g
plu
g
fOI
flo
w
co
ntr
ol.
O
ff-s
tate
fo
r th
e
pu
lse
OC
CU
rs
by
sig
nali
ng
th
e
hy
dra
ul
ic
actu
dto
r to
fI
lQ')
{,
the
mete
rin
g
plu
g
to
seal
off
g
as
flo
w at
lile
!l
OL
z)e.
T
ills
d
ev
iLe "n
l
be
use
d
for
eart
hq
uak
e
and
au
ti-e
art
hq
uak
e
iuv
"o
tlg
.1li
on
s o
n
the
str
uctu
re
sho
wn
in
F
igu
re
12
at
the
Un
ivers
ity
o
f C
.lif
o!u
,.,
Berk
ele
y.
n:ST~
III r
\IJ'~l.SE
GE~~
.:~T
O!{S
A 2
0,0
00
Ib
sh
ock
is
ola
ted
co
,,[r
ol
room
(~O
ft
x 5
0
ft)
fo
r.
po
wer
p
)all
l w
as
teste
J
wh
ile
/un
cti
on
all
y o
pera
tin
g
to
ind
uce
mali
on
-tim
e
his
tori
es
ex
pecte
d
frol
ll
a sp
eC
ifie
d
base
m
oti
on
h
azarJ
[IO
}.
One
o
f th
e
fou
r p
uls
e
gen
erd
tors
u
:""j
i"
p
ictu
Led
in
F
igu
re
21
. T
he
sp
ecif
ied
p
uls
e
lrain
.u
d
the
fou
r "I
t'as
llr"
d
on
es
are
p
rese
nte
d
ill
Fig
ure
2
5.
Ty
pic
al
",ed
sure
d
tran
sfe
r tu
ncti
on
s
of
the
str
uctu
re
ule
d
to
calc
ula
te
the
pu
lse
train
are
p
rese
nte
d
in
Fig
ure
2
6
and
in
clu
de
tran
sfe
r fu
ncti
on
m
ag
nit
ud
e,
ph
dse
, an
d
iurp
uls
e fu
ncti
on
. ~Iagnitude
un
its
are
th
e
rati
o
of
dccele
ra
[1"1
1
to
/urc
e
dS
fu
ncti
on
o
f fr
eq
uen
cy
. T
he
pre
dic
ted
co
ntr
ol
roou
r
100,
c ... ~ ~
FO
RC
E
PU
LSE
TR
AIN
GE
NE
RA
TO
I{S
,1:.66
"' (1
2tt
l"1
t·
8 m
ci
I (6
f.ii
'
rl~
_d h
--..
"'.,;;;1
J .... -
Rl
PUlS
ER
.~ I
1 ,_
. ,U
lS
ER
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s.]
m -'
t ,,
~, ,
" I
(17
.]
ttl,
/
1.2
] H
I
l~owm"'.
~ R
R
7 .~s
HI
lS.8
HI
AH
~O.l
H.
78.4
HI
fflO
NT
ELEV
ATI
ON
Sl
OE
EL
EVA
TIO
N
FIGU
RE
12.
uca
TEST
ST
RUCT
URE
fIGU
RE
13.
MODE
SH
APES
Of
UCB
FRAM
E DE
TERM
INED
BY
SA
P6
PULS
E TR
AIN
ON
]R
O
flO
OR
~
~
0
e
IS T
flO
OR
'JTW1~
~r -1
00
I -~
~-"r
---.
...-
-i--
,..-
-r
o T
IHE
. ,
Tlt
tf I
•
FIGU
RE
IS.
TRAN
SIEN
T SI
NU
SOID
AL
MOT
ION
ON
FIR
ST
FLOO
R
7'J
FIGU
RE
14.
FORC
E PU
LSE
TRAI
N LO
CATE
D ON
3R
D fL
OOR
Of
UCB
STRU
CTUR
E TO
IN
DUCE
TRA
NSIE
NT S
INU
SO
I DA
L M
OTI O
N
Of
UCB
STRU
CTUR
E IN
DUCE
D BY
PU
LSE
TRAI
N AT
AIR
(U~HIOH
PRE~SURE
SOU
RCE I
ARRl~T
/EN
T
1iJ
r'l (01
L __
~TIOH
.L..l
.L.L
1 __
--I
OL
lIIO
ER
'-
----
----y-------'
OR
IVIN
G
AND
CUIIT
ROL
~V~TEM
2.23
Hz
O
f FI
G;
13
MAN
OREL
CU
TT 'H
G
TOOL
~
Ill'
M
ACH
I HE a
!lOLO
ER
PUL~E
TRA
IN
~t..ll
l po
16.
TIM
£
fOR
CE
PUL~E
TRA
I H
TEST
IN
PUT
FIGU
RE
16.
PUL5
E-FO
RI1I
NG
DE
VICE
\I/T
il DR
IVIN
G At
JO
CONT
ROL
SYST
EM
MAX
IMUI
1 OU
TPUT
8
,00
0
Ibf
KO ~
I w
ffi
DY
NA
MIC
RE
SP
ON
SE
OF
ST
RU
CT
UR
ES
fiGU
RE
17.
~ r'
d r-,-"
'0
_ I.
~
[ r·
~~""
'~~
recd
II t~
1
~[
----
__ G
Uill
OT
INE
FR
AME
ell
.~~~CABLE
CABL
E C
UTT
ER
G
UID
E
RODS
.---G
U I
DE
__ ~D
ROP
CA
RR
IAG
E
_P
UL
SE
C
UTT
ER
~ ~NUBBIN
/Nu
a6
IN
t10L
DE
R
SKET
CH
O
f liE
D/U
K-f
OR
CE
O
UIP
UI
PULS
E G
ENER
ATO
R M
AXIM
UM
OUTP
UT
16,0
00
ft-l
b
AND
1,80
0 Ib
f-s
CA
RR
IAG
E
3.05
rn
(10
.0
f t)
MAN
ORE
L
~-.~ .
. 2.
87 ,
,, .. -
---1
(~
. 1
,2
f t)
FIG
UH
[ Il
l.
ASSE
MBL
Y -
IMPU
LSE
TEST
ER
MAX
IMUM
OUT
PUT
54
,00
0
ft-I
b
AND
11,]
00
Ibf-
s
FO
RC
E
PU
LS
E TI~AIN
GE
NE
J{A
TO
RS
REA
CTA
NC
E/TE
ST
STRU
CTU
RE
,/ HY
DRA
ULI
CR
AM
r' fO
RC
E C
Ell
~~2 ST
EEL
SlaC
KS
(ISO
LATO
R
REP
LAC
EMEN
T)
(QU
AD
-PO
D) RE
ACT
I V
ElT
E 5
1 ST
RU
CTU
RE
7-11
}'
(IIP
PRO
X)
T
2-1
/2 •
(APP
l\OX
)
)///
//h
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hW
7d
kw
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//h
00
0//
,V,w
Md
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' /1
EQ
UIP
ME
NT
RACK
(C
Ul
oo
IlN
)'
(APP
RO
X
) fT
HIG
II)
/4
ST
EE
l H
aUN
TIN
G
BLO
CKS
II'
'1/
(ISO
LATO
R
REP
LAC
EMEN
T)
I I
I ...
.-tIO
UIIT
lNG
eA
SE
~-~--S.S' (A
PP
RO
X\-----l
FIG
URE
19
. BI
AX
IAL
TEST
FA
CIL
ITY
CO
NFI
GU
RATI
ON
M
AXIM
UM O
UTPU
T 15
,000
Ib
f EA
CH
AX
IS
PROG
RAM
S
I GH
ALS
-@
I-----
QJfi
I.l J~ S
ERVO
S
LAV
E
VA
LVE
P~OGRAH
~
,,----
SE
RV
O
PIL
OT
VA
LVE
SIG
NA
LS I
V
OIC
E C
OIL
fiGU
RE
20
. PR
OGRA
MKA
BLE
GAS
PULS
E GE
NERA
TOR
COLD
GA
S SY
STE
M-
500
TO
10
,00
0
Ibf
I
III
IQ
DY
NA
MIC
RE
SP
ON
SE
OF
ST
RU
CT
UR
ES
FIGU
RE
21.
APPL
ICAT
ION
OF P
ULSE
GE
NERA
TOR
(SEE
FI
G.
16)
FOR
EQUI
PMEN
T TE
ST
ACCE
LERA
TION
-TIM
E H
ISTO
RIES
FIGU
RE
22.
PULS
E GE
NERA
TOR
:r w
-...J
FIGU
RE
23.
LARG
E PU
LSE
GENE
RATO
R fl
GUR
E 24
. (S
EE
FIG
. 18
) US
ED
TO
MEA
SURE
TR
ANSF
ER
FUNC
TION
S AN
D MO
DE
SHAP
ES O
F LA
RGE
STRU
CTUR
ES
(SEE
FI
G.
17)
USED
FO
R TR
ANSF
ER
FUNC
TION
AN
D MO
DE
SHAP
ES O
F ST
RUCT
URE
ai-A
XIA
L PU
LSE
GENE
RATO
R (S
EE
FIG
. 19
) FO
R EQ
UIP
M
ENT
TEST
S AC
CELE
RATI
ON
TIM
E H
ISTO
RIES
FOR
CE
P
ULS
E T
RA
IN G
EN
ER
AT
OR
S
113
2400rl---~--~-------'
2000
~
1600
\j
1200
at
! ~
800
400 .I JI
IJIIIIIIII
II~ till ~
II I
o 0
.16
0
.32
0
.,.8
0
.6"
TIM
E,
5
(a)
Spe
cifi
ed p
ulse
tra
in f
or e
ach
corn
er
1500]
JLJA
' 15
00
~ 10
00
;!:! •
1000
'" at
! .
U
~
500
at!
500
0 ... o
I IIt
AIIH
1.'Ul
-J., "
I
0
(b)
Tes
t pu
lses
at
SW c
orne
r (c
) T
est
puls
es a
t Sf
co
rner
1500
15
00
.Q
;!:!
1000
..;
U
at
! 50
0 0 ...
..;
1000
u at!
500
0 ... 0
0
. o
0.2
O.~
0.6
o
0.2
0
."
0.6
T
IME
, j
TIM
E,s
(d)
Tes
t pu
lses
at
HE
corn
er
(e)
Tes
t pu
lses
at
NW c
orne
r
FIGU
RE
25.
200,
000
LB
SHOC
K IS
OLAT
ED C
ONTR
OL
ROOM
PLA
TFOR
M:
SPEC
IFIE
D A
ND A
CTUA
L TE
ST-IN
PUT
PULS
ES
USIN
G fO
UR
PULS
E GE
NERA
TORS
SH
OWN
IN
fiG
. 21
Mol
DY
NA
MIC
RE
SP
ON
SE
OF
ST
RU
CT
UR
ES
N o
} -4
. .. -L
--.1
-_
_ .L
_---4
---L
__
.l_
2·
d ..
200
400
600
800
fREQ
UEN
CY,
H
z
(a)
Tra
nsfe
r fu
ncti
on m
agni
tude
O+I--~~~~--~~--~--~-+
>C
-100
'" " ." ... !2 -2
00
:z:
Q
.
ll>'
-)0
0
I;
0 w
0
0 I
(b)
)0
20
10
· -;:
;
200
400
600
800
fREQ
UEN
CY,
H
z
Tra
nsfe
r fu
ncti
on p
hase
-;;
O~I
-10
-20
-)0
0
(c)
FIGU
RE
26.
0.5
1.0
TI
ME,
•
1.5
Impul~e
func
tion
2.0
CONT
ROL
ROOM
: M
EASU
RED
TRAN
SFER
fU
NCTI
ON
fOR
0.5
Hz
TO
500
Hz
80
--,_
... -
, ,.
-. "l-"--r--T--~
N ..
60
.....
c 40
Z
0
20
t- .. a:
0 ... -' ... u u
-20
.. ~
-40
+--
,--.
--'-
,--,
., --
r--,
...-
---r
--0
0.1
6
0.)
2
0.4
8
0.6
4
Til
lE.
s
(a)
Pre
dict
ed
120 r--;r-~---r--~--r--'---T
N ..
80
.... .: z 40
0 t-O
~ ...
-40
-'
... u ~~~~
II~I"
I u
-80
.. -1
20
N .. ....
0 0
.16
O
. )2
Til
lE,
5
0.4
8
(b)
Pul
se s
imul
ated
0.6
4
.: :1 I.
,
~ o~
S -4
0 r ...
. 'iJ~""b"
lv;lA ...
.. .-...
__
---
... -'
w
u u o-o~
0:6
0
:8
1:0
..
fiGU
RE
27.
TIM
E,
•
(c)
Pul
se
test
ed
CONT
ROL
ROOM
PLA
TFOR
M:
ACCE
LERA
TION
-TIM
E .
HIS
TORI
ES
OF P
RED
ICTE
D,
PULS
E-SI
MU
LATE
D,
AND
PULS
E-TE
STED
M
OTIO
NS
FO
RC
E P
UL
SE
TR
AIN
GE
NE
RA
TO
RS
M
5
PU
LSE
R A
CC
ELE
RO
ME
TE
RS
(T
yP)
1!;'t
WI.=
t
I I.,m----------~
(13
8.6
11
)
FIGU
RE
2B.
CROS
S SE
CTIO
N OF
NUC
LEAR
PR
OCES
SING
PLA
NT
SHOW
ING
ACCE
LERO
MET
ER A
ND
PULS
ER
LOCA
TION
S (P
ULS
ER
EXC
ITA
TION
NO
RMAL
TO
SEC
TION
SH
OWN)
z uI
o ~ (a)
Z uI
0 0: fl
.10
6
• 1
0·
l ~-
.:-~
T .~'
-~r-l: ~
o :5 II
.
-I
-2
-L
-..
J. _
_ .l.
__
.1 _
_ J
____
..L
.--1
.
0.2
0
.3
0.4
0
.6
TIM
E,
lec
Raw
inpu
t fo
rce-
tim
e h
isto
ry
.10
· •
10
·
"~r;
;;;~
co ..
3 B
·2
uI
O
F M
AS
S O
N
0 6
LOA
D C
Ell
0:
0 A
II
. 0 0
(b)
Fil
tere
d
inpu
t fo
rce-
tim
e h
isto
ry
(0
to 2
0 H
z)
OJ
EX
PE
RIM
EN
TA
L
~I.O
. ...
--
~ r6
~ L
___ -
L _
_ ~~;; _
_ ~_-_--
~. 0
' N
OD
ES
:c FI
GURE
29
. TY
PICA
L MO
DE
SHAP
E PL
OT
FROM
EXP
ERIM
ENTA
L AN
D AN
ALYT
IC
DATA
(F
requ
ency
: 9
.2 H
z)
(d)
Z
10,
~'"
6 0
( 0
~:o~lfiI
OJ aL
'
8 -6
..
o 1
._:'
.--
1-'
__
J __
__
...J.
0.2
0
.4
0.8
0
.8
1.0
U
TIM
E.l
8c
(c)
Acc
eler
atio
n-ti
me
his
tory
(0
to
20
Hz)
! _8~--
alO
11 __ .
__ . __
.s __
z·
-1
0(1
0 _
._
Ii: __
_ ....
----.1
0
OJ
1.0
iI! 0.
1 F
RE
QU
EN
CY
. H
.
10
-1
:!! a iii
10
-8 ~
0( t o:
10
-6 ~
Tra
nsfe
r fu
nct
ion
'(ac
cele
rati
on
di
vide
d by
fo
rce)
FIGU
RE
30.
TYPI
CAL
DATA
RE
CORD
S fR
OM P
ULSE
TR
AIN
TEST
S AN
D RE
SULT
ING
TRAN
SFER
(IN
ERTA
NCE
) FU
NCTI
ONS
COM
PUTE
D FR
OM D
ATA
-PU
LSE
GENE
RATO
R SH
OWN
IN
FIG
S.
1B A
ND
23
:v I w ~
!I(,
DY
NA
I\II
C
RE
SI'
ON
SI'
O
F S
TR
UC
TU
RE
S
II",
t101
1 d
"e
to
b ..
,,<:
IIlI
ltio
" h"
ZiJ
l-d
is
giv
en
il
l F
igu
re
27
to
geth
er
wit
h'
cOlI
Il'u
ted
l'ul6
<:
:;i"
"date
d
II,u
tiol
l an
d
mo
tio
ns
mea
sure
d
du
rin
g te
sts
w
ith
L
he
pu
l""
g"n
er.
tto
rs.
Teo
ts
ot
a la
rge
nu
cle
ar
pro
cess
ing
p
lan
t w
ere
per
form
ed
to
ob
tain
tr
au
sfe
r fu
ncti
on
s au
d to
ex
trd
ct
bu
ild
ing
mod
es
alld
d
am
pin
g{
IlJ.
D
ue
"I
tl
te
l)ll
i Id
illg
s te
sted
w
as
a re
info
rced
co
ncre
te
stru
c!.
ure
40
ft
h
igh
, 13
L ft
w
ide,
au
d
30
0
ft
lon
g.
Fig
ure
29
is
a
typ
ical
mod
e sh
ape
ex
Lr.
ete
d
from
th
e
pu
lse
gen
era
ted
d
ata
g
iven
in
F
igu
re
30
. T
he
pu
lse
gen
er.
tor
Ilse
d in
th
ese
te
sts
is
sh
own
in F
igu
res
18
and
2
3.
AC
KtH
Jl-JL
UlG
tlEN
TS
Tl,
is
stu
dy
w
as
sup
po
rted
in
p
art
b
y
the
Un
ited
S
tate
s N
ati
on
al
Sci"
"ce
Fo
un
dat
ion
u
nd
er
Gra
nt
No.
P
FR
77-1
5010
. T
he
ass
ista
nce
and
g
uid
.".-
" p
rov
ided
by
D
r.
Joh
n
B.
Scalz
i is
g
reatl
y
ap
pre
cia
ted
.
HEF
EHEN
CES
-~-----~-~-
I.
!ill
ttu
fti,
F
.B.
and
M
air
t,
S.f
. h
Au
llly
tical
an
d
Ex
peri
men
tal
Stu
dle
i o
f •
Ht:
ch
lnlc
.. l
Pu
lae
(;en
cIM
lor,
" ~~!_~L!.!!8.:-_!~~~!!!.~~!!!~SHEi-~~!~l!,
96
;2,
Ha
y )9
74
, p
p.
4~9-470.
2.
Hasri
, S
.Y.
i ~e~~y,
G.A
.i
All
J S
Mff
orJ
, f.
b.
l'An
Ad
up
liv
e
Ran
dom
Sr~rctl
Met
ho
d
(0£
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«:H
liti
c ..
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ll
of
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ge Sc.l~
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nli
near
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ltl!
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~i'~~~r~ r~~~~~~~! t~~!~!.!.~,
lnt.
F
ed
era
tio
n
of
Au
tom
ati
c
Co
ntr
ol,
T
bil
isi,
U
SS
R,
So
p
19
16
.
] .
4.
H.u
ri,
S.L
an
d
Sli
tto
rd,
f.iL
"D
ynli
llll
c I:
:nv
lro
nm
cnt
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ula
tio
n
lIy
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~.
Tech
niq
uelj
,"
r~~~_:.
AS~~
I~s,
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,(:!
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!~,,
-,-
101;~l1t,
Feo
1
97
6,
pp
. 1
51
-16
9.
Hut
£r1,
S
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11
1111
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T.H
. "A
N
OH
l)in
un
etd
c
Iden
tif!
clI
lio
n
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niq
ue
foe
No
nlt
ot!
ar
DY
lJn
lDi(
l'
IDh
lcm
lj,"
:!!~!_..9!_!-J!l!!.:-1!!~:..~~~,
1.6
:2,
Jun
19
19.
~.
Hd
l;ri
I S
.t'.
an
d
Saff
urd
, F
,B.
"Eart
hq
uak
e
En
vir
olu
uen
t S
iall
illl
tio
n
by
Pu
lue
Gt!
nera
loca,"
E£~~:..._l~~~~~~!!!.f2!!!..,:_~!!_~!!!~quake.!.~.H.:.
l.ta
nb
ul,
T
uck
ey
. S
ep
8-1
3,
1980
.
6.
CIO
II!1
U,
H.W
. ~l
Hd
Tan
g,
n.T
. ~~
~t!~
ll~~
~~_S
i~l!
!~~~
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~~l_.~~-!
~!:~!_~'!:~~~
~~~~
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l!.!
) V
ol.
1
. E
ER
e 1
56
. B
erk
ele
y,
CA;
Un
iv.
of
ClS
lif.
E
arth
qu
llk
e EU~lnecring
Cen
ter,
1
97
).
S,d
ford
, L
B.
~!.!~~!:!'!~!
~f ~~
!~!:
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~~~~
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l'!~
~~ ~~~!~~~
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~!':!~ ~~
~~~~
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~I
U.S
. N
ati
on
al
Scie
nce
r'o
lili
dati
on
G
ran
t N
o. ~rH77-15010,
lI.b
hll
lglo
n,
D.C
.,
19
76
.
8.
H':
Hir
i,
S.F
. i
Bek
ey,
G.A
.;
So
ffo
rdt
F.B
. i
and
Oe
lq~.
hlln
ydr,
T
.J
rlA
nlf
-[.I
rth
qu
dk
c
AP
l-d
icl:
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n
of
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lilc
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en
crd
tora
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y C
on
fere
nce, Allant~,
GA
. Ja
n
19
81
.
9.
SIl
Uo
rd,
F.B
. "H
ecll
un
ic..
:al
t'o
rl:e
P
ul"
c
Geu
ecd
tor
for
Uue
in
S
tru
ctu
ral
Au
alY
I:iI
M,"
U
.S
Patc
ill
Off
ice
No.
~,020,672,
Hay
1
97
7.
10
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vrJ
, L
B
el
Ill.
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lr-I
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t C
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un
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hu
ck
S
imu
lati
on
T
e)jt
lllK
o
f H
ati!
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bluq
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nl
by
h
ll)j
e
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nlI
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rtif
illd
l1o
ll)j
tul"
valt
nin
gen
, S
tock
ho
lLO
, S
wed
en,
H.JY
23-26~
19
17
.
11
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lcH
, D
.G
iUlt
1 ~:ll:IttOl"J)
F.l
:\
"Hcd
6u
rcm
eu
t o
f D
yn
amic
S
tru
clu
ca)
Ch
",r
lH:l
e.n
atJ
cti
o
f tt
"bid
ve
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ild
ing
ll
by
H
igh
-1.«
:vel
H
Lil
lip
lc
l't:
ch
ni(
Iut:
H,"
S
ho
tk
&
Vth
rtat
ioll
BLlll.~
SO
, S
VIC
\Ja~hllq~lon,
nc.:
N..t
.vll
l N
elil
. L
tall,
1
98
0.
-------------~--------.
P I
,j::
.
o
Pro
ceed
ings
of
the
Sec
ond
Spec
ialty
Con
fere
nce
on
Dyn
amic
Res
pons
e of
Str
uctll
res:
E
xper
imen
tatio
n, O
bser
vatio
n,
Pred
ictio
n an
d C
ontr
ol
Org
aniz
ed b
y th
e E
ngin
eerin
g M
eclla
nics
Div
isio
n of
the
A
mer
ican
Soc
iety
of
Civ
il E
ngin
eers
CO
-SP
ON
SO
RE
D B
Y:
AS
CE
/EM
D T
echn
ical
Com
mitt
ee o
n E
xper
imen
tal
Ana
lysi
s an
d In
stru
men
tatio
n A
SC
E/E
MD
Tec
hnic
al C
omm
ittee
on
Dyn
am
ics
AS
CE
/ST
D T
echn
ical
Com
mitt
ee o
n D
yna
mic
EH
ects
E
arth
qu
ake
Eng
inee
ring
Res
earc
h In
stitu
te
Nat
iona
l S
cie
nce
Fou
ndat
ion
Str
uctu
ral
Eng
inee
rs A
ssoc
iatio
n of
Cal
iforn
ia
Win
d E
ngin
eeri
ng R
esea
rch
Co
un
cil
Ge
org
ia I
nstit
ute
of T
echn
olog
y, S
choo
l of
Civ
il E
ng
ine
eri
ng
Gar
y H
art,
Edi
tor
JA
NU
AR
Y 1
5-16
, 19
81
Sh
erat
on
, A
tlan
ta
AT
LA
NT
A,
GE
OR
GIA
Pu
t)lis
ho
d b
y Il
le
z (j)
hj
G1
Ii
AI
::l
rt
o trJ
trJ
I ---.J
---.J
I-'
U1 o I-'
o
Am
eri
can
So
cie
ty 0
1 C
ivil
fn[)
lfle
erS
3
45
Eas
t 47
1h S
lIo
el
No
w Y
urll.
No
w Y
ork
1001
7
~ I ~
......
AN
TI-E
ART
HQ
UA
KE
APP
LIC
ATI
ON
O
F PU
LSE
GEN
ERA
TORS
by
1 2
3 4
Sam
i F
. M
asr
i, G
eorg
e A
. B
ekey
,
Fre
der
ick
B.
Saff
ord
, T
ejav
J.
Deh
ghan
yar
Ab
stra
ct
Th
is
pap
er is
co
nce
rned
wit
h a
fe
asi
bil
ity
st
ud
y in
to
the
use
of
serv
oco
ntr
oll
ed g
as
pu
lse
gen
erat
ors
to
mit
igate
th
e ea
rth
qu
ake-
ind
uce
d
mot
ions
o
f ta
ll b
uil
din
gs.
A
sim
ple
yet
reli
ab
le o
n-l
ine a
cti
ve c
on
tro
l al
go
rith
m i
s d
evel
op
ed a
nd
app
lied
, by
m
eans
o
f n
um
eric
al s
imu
lati
on
st
ud
ies,
to
a
mod
el
of
an e
xis
tin
g s
teel
fram
e st
ructu
re.
The
co
ntr
ol
con
cep
t is
sh
own
to b
e eff
ecti
ve in
co
ntr
oll
ing
th
e re
spo
nse
of
lin
ear
as
wel
l as
n
on
lin
ear
bu
ild
ing
sy
stem
s un
der
dyna
mic
ex
cit
ati
on
.
Intr
od
uct
ion
• A
nal
yti
cal
and
exp
erim
enta
l st
ud
ies
[1,2
] h
ave
show
n th
at
amon
g th
e cla
ss
of
pas
siv
e au
xil
iary
m
ass
dam
pers
u
sed
fo
r v
ibra
tio
n c
on
tro
l,
the
imp
act
dam
per,
w
hich
is
a
hig
hly
no
nli
nea
r v
ersi
on
of
such
d
evic
es,
has
a su
peri
or
per
form
ance
rec
ord
co
mpa
red
to
the
con
ven
tio
nal
dyn
amic
v
ibra
tio
n n
eu
trali
zer
whe
n u
sed
und
er d
ynam
ic
env
iro
nm
ents
re
sem
bli
ng
ea
rth
qu
ake
ex
cit
ati
on
s.
How
ever
, du
e to
th
e tr
an
sien
t n
atu
re o
f eart
h
quak
e gr
ound
mo
tio
ns,
th
e im
pu
lsiv
e fo
rces
im
par
ted
by
the
imp
act
dam
per
to
the
prim
ary
stru
ctu
re
(see
F
ig.
1)
do
no
t al
way
s o
ccu
r at
the
opti
mum
ti
me
from
th
e m
otio
n re
du
ctio
n p
oin
t o
f v
iew
. C
on
seq
uen
tly
, th
e eff
ici
ency
of
the
imp
act
dam
per,
li
ke
that
of
oth
er
sim
ilar
pas
siv
e da
mpi
ng
dev
ices
, is
su
bst
an
tiall
y
redu
ced
com
pare
d to
it
s eff
icie
ncy
u
nd
er p
eri
o
dic
ex
cit
ati
on
. I
A c
urr
en
t re
sear
ch e
ffo
rt
[3]
is
con
cern
ed w
ith
th
e v
ali
dati
on
of
the
con
cep
t o
f u
sin
g p
uls
e te
chn
iqu
es
[4]
to s
imu
late
th
e re
spo
nse
of
stru
ctu
res
to a
rbit
rary
dyn
amic
en
vir
on
men
ts
[5].
In
th
e co
urs
e o
f th
is
stu
dy
, (1
) an
eff
icie
nt
alg
ori
thm
has
be
en d
evis
ed
for
det
erm
inin
g
the
opti
mum
fo
rce
pu
lse-t
rain
ch
ara
cte
rist
ics
to b
e ap
pli
ed a
t d
iffe
ren
t lo
cati
on
s in
th
e st
ructu
re s
o a
s to
mat
ch
the
cri
teri
a r
esp
on
se
[6),
an
d (2
) ga
s p
uls
e g
ener
ato
rs,
empl
oyin
g d
igit
al
serv
oco
ntr
oll
ers
and
h
yd
rau
lic
actu
ato
rs
in c
on
jun
ctio
n w
ith
a
gas
sto
rag
e sy
stem
and
a
no
zzle
wit
h
a m
eter
ed
flow
to
fu
rnis
h
the
need
ed
thru
st,
are
bei
ng
bu
ilt.
1 Pro
fess
or,
S
choo
l o
f E
ng
inee
rin
g,
Un
iver
sity
of
So
uth
ern
Cali
forn
ia
2 Pro
fess
or,
S
cho
ol
of
En
gin
eeri
ng
, U
niv
ersi
ty o
f S
ou
ther
n C
ali
forn
ia
3 Ass
oci
ate,
A
gbab
ian
Ass
oci
ates
, E
l S
egun
do,
Cali
forn
ia
4 .Gra
du
ate
stu
den
t,
Sch
ool
of
En
gin
eeri
ng
, U
niv
ersi
ty
of
So
uth
ern
Cali
f.
Num
bers
in
br~ckets
des
ign
ate
item
s in
th
e re
fere
nce
lis
t.
87
ilK
DY
NA
MIC
RE
SP
ON
SE
OF
ST
RU
CT
UR
ES
In v
iew
of
the
pre
ced
ing
dis
cu
ssio
n.
this
p
aper
is c
on
cern
ed w
ith
a
stu
dy
o
f th
e fe
asi
bil
ity
o
f u
sin
g s
erv
oco
ntr
oll
ed g
as
pu
lse
gen
erat
ors
to
m
itig
ate
the
eart
hq
uak
e-in
du
ced
o
scil
lati
on
s o
f ta
ll b
uil
din
gs
or
sim
ilar
stru
ctu
res.
Co
ntr
ol
Alg
ori
thm
A r
ecen
t st
ud
y b
y th
e au
tho
rs
[7]
pre
sen
ted
a
rela
tiv
ely
sim
ple
on
li
ne p
uls
e co
ntr
ol
alg
ori
thm
su
itab
le
for
use
wit
h d
istr
ibu
ted
p
aram
eter
sy
stem
s su
bje
cted
to
arb
itra
ry n
onsta~ionary d
istu
rban
ces.
T
he
mai
n id
ea
of
the
alg
ori
thm
is
that
reso
nan
ce p
heno
men
a ca
n b
e el
imin
ated
. o
r at
least
dra
stic
all
y
red
uce
d.
by disorgani~ing
the
ord
erly
and
g
rad
ual
b
uil
du
p
of
the
stru
ctu
ral
dyna
mic
re
spo
nse
by
ti
med
fi
rin
g o
f a
pu
lse
of
suit
ab
le m
agni
tude
ap
pli
ed
in
the
pro
per
dir
ecti
on
. F
urt
her
mo
re,
in
ord
er
to m
inim
i~e
the
amou
nt o
f co
ntr
ol
ener
gy
uti
li~e
d.
the
co
ntr
ol
forc
e sh
ou
ld b
e ap
pli
ed o
nly
whe
n th
e st
ructu
ral
resp
on
se e
xce
eds
a cer
tain
th
resh
old
le
vel
rela
ted
to
th
e re
sist
an
ce o
f th
e st
ructu
re.
ASl
jum
e.
as a
fi
rst
ord
er a
pp
rox
imat
ion
. th
at
the
stru
ctu
re
to b
e co
n
tro
lled
is
m
odel
ed a
s an
eq
uiv
alen
t li
near
sin
gle
-deg
ree-
of-
free
do
m (
SDO
F)
syst
em a
s sh
own
in F
ig.
2.
Sup
pose
th
at
at
tim
e t
~ to
' th
e th
resh
old
b
arr
ier
has
be
en e
xce
eded
. T
hen·
th
e ex
pec
ted
val
ue
of
the
resp
on
se,
unde
r th
e as
sum
pti
on
th
at
the
ex
cit
ati
on
is a
~ero-mean
rand
om p
roce
ss,
is g
iven
by E
[y(t
)]
~ y
u(t
-t
) +
y v(
t -.t
) +
x (t
) o
0 0
0 p
whe
re u
(t)
v(t
)
x (t
) p h(t
)
p(t
)
wd
w
1;
exp
(-tw
t)(c
os
wdt
+ ~ s
in w
dt)
d
1 --
exp
(-tw
t) si
n w
dt
wd
.
J(T
o h
(t -
t)
p(t
)dt
a
Imp
uls
ive
resp
on
se o
f th
e sy
stem
G
vet)
Imp
uls
ive
co
ntr
ol
forc
e o
f d
ura
tio
n
Td
and
peak
lev
el
Po
wh-?
" F
unda
men
tal
freq
uen
cy o
f th
e sy
stem
Rat
io o
f cri
tical
dam
ping
of
the
syst
em
(1)
(2)
(3)
(4 )
(5)
(6)
(7)
(8)
(9)
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T
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DY
NA
MIC
RE
SP
ON
SE
OF
ST
RU
CT
UR
ES
Th
e co
st
fun
cL
lon
to
b
e
min
imiz
ed
w
ill
be
!lele
cte
d
as
J(p
)
ftfl
2 o
op
t(E
[y(t
)]l
dt
t o
wi"
"."
To
pt
is
the
op
tim
izati
on
p
eri
od
, ch
ose
n
to
be
O(T
),
wil
h
T
b"lnl~
thl!
fu
nd
i.ll
llen
tal
pel"
iod
o
f th
e
!ly
st"l
Il.
(10
)
[lu
e lo
lh
t.!
natu
re
of
the
ex
pre
ssiO
n>
; fo
r u
, v
, an
d
x ap
peari
ng
In
E
q.
I,
Ie'!.
10
can
b
e
an
aly
ticall
y
ev
alu
ate
d
an
d
dlf
feren
tfate
d
to
yJeld
ti
le
opti
lilu
IU
pil
ls"
am
pli
tud
e
PO
pt
wh
ich
w
ill
min
imiz
e
J(P
o)'
Th
e re
~ull
I n~
dn
,Jly
ticd
l ex
pre
ssio
n
for
P op
t w
ill
inv
olv
e
sim
ple
alg
eb
raiC
l!
xp
res"lo
ns
(\Jh
ich
n
eed
to
b
e
ev
alu
at"
d
on
ly
on
ce
for
a g
iven
sy
st"m
) IH
II1
Llp
lyin
g
the "il
liti
al"
d
bp
lacem
en
t an
d v
elo
cit
y
Yo
an
d
Yo
' T
hu
s,
un
ce
a co
ntr
ol
pu
lse is
call
ed
fo
r,
vir
tuall
y n
eg
lig
ible
co
mp
uta
tio
nal
d lu
rL
l.tI
lel
hL
'ne"
, co
ntr
ol
iag
li
me)
is
need
ed
to
d
ete
rlil
ine
the
op
tim
um
p
uls
e
IIlol~
lIi L
ud
" ,
dl1
'elO
tio
n,
an
d
tili
lin
g.
Th
is
usefu
l fe
atu
re
of
the p
ro
I'"s
ed
cO
lltr
ol
.dg
ur
1t1i
1ll
i"
ulg
nif
ican
t in
as,;
essin
g
Lh
e feasib
ilit
y
of
lile
II
I"ti
lud
fo
r o
n-l
in",
imp
lem
en
tati
on
.
A...
l'~l
lio~
U!2I
~
Til
e u
tili
ty
of
till
'! p
rop
ose
d
meth
od
w
ill
now
b
e
dem
on
str
ate
d
by
"p
ply
llig
it
to
a th
ree-d
eg
ree-o
f-fr
eed
om
mo
del
of
a th
ree-s
tory
ste
el
:P'
frd
llle
(F
ig.
3)
that
has
been
,,
"ten
o>
lvely
stu
die
d,
bu
th
"n
.aly
ticall
y an
d
I l·
xp
eri
llle
n[,
il.l
y
[8,9
] at
lite
U
niv
ero
>it
y
of
Cali
forn
ia,
8erk
ele
y
(UC
ll).
.1'-
W
ASS
UII
Il!
thal
a sin
gle
p
uls
e
co
ntr
oll
er
is
locatl
'!d
at
thl!
fir
st
slo
ry
of
lilb
str
uctu
re
an
d
tlta
t th
e
lhre
sh
old
le
vels
fo
r tr
igg
eri
ng
ti
l" ",,
"tr
oll
er arc
In
.!f
~ {
0.6
4,
0.8
8,
1.0
).
Usi
ng
a
recta
ng
ula
r p
uls
e
of
du
raL
lulI
'I'
d ~
0.0
1
sec
an
d
an
o
pti
miz
ati
on
p
eri
od
T
op
t -
0.5
sec
resu
lts
III
thl'!
cO
I1ll
'oll
ed
re
sp
on
se
sho
wn
in
F
ig.
6.
Co
rresp
on
din
g
resu
lts
for
tl sin
gle
co
ntr
oll
er
locati
on
at
0i2
an
d at
n1J
are
sh
ow
n
It,
Fll
\s.
7 ,w
d
H.
CU
IIII
"lri
ng
FIg
s.
b,
7,
alld
e,
it
i:>
seen
th
at
rcg
ard
le:;
s
of
the
co
n
lr,d
lt'r
b
H:a
tio
ll,
Lilt.
! rl
.!~{
Jon!
le
of
c ....
ch
m
ass
is
k
ep
t nt
!<.u
-ly
lJo
llll
llcd
b
y
the
~ele
LI"d
th
resh
old
le
V"l,
..
llo
\Jev
er,
fr
om
th
e
co
ntr
ol
ell
"rt;
y
po
int
of
vl"
\J,
slg
niU
IOu
llt
red
ucti
on
in
th
t.!
req
llir
ed
im
pu
lse
can
b
" ach
l"v
ed
if
tile
IH
ilsl
! b
'!i,
era
lor
is
locate
d
dt
the
top
fl
ou
r,
ralh
"r
thd
n
tlte
lu
wer
flu
or
of
the str
uctu
re.
Th
e o
pti
mll
l\l
locati
on
o
f p
liis
e
gen
era
tors
is
b
ein
g
::>
luJl
ed
as
a re
f iU
l.!l
Ile
nt
to
co
nsc
:rv
e
imp
uls
e
rcqu
ll-t
.!II
It.!
lllS
.
Til
e re
laL
lve
velu
cit
y
r"sp
on
se
of
the
str
uctu
re w
llh
an
d
wil
hu
llt
cU
lltr
ul
b sl
tmJ\
1 II
I F
ig.
9.
No
te
that
in sp
ite
of
the
tr,.
III"
icn
ts
co
rre
SI'
Ull
Lli
llg
tu
Lhe
cO
lltr
ul
pu
!,;"
,;,
su
b,n
an
rial
red
ucti
oll
il
l L
h"
velo
ciL
Y
is
ub
Ull
led
10
1 Ll
i "
sjn~le
,:u
ntr
ull
er.
Thl~
r;.:
lalh
.'t.
! d
L.p
iJct
.!lJ
\(:n
l re
spO
lltit
..!
of
the
salli
e ti
tflH
:tu
re
, w
Ith
th
e
!:ld
lllv
l:u
lllr
oll
cr
Pd[u
l!lI
~ll.
!rS
useJ
in
Fig
s.
b th
rO
llg
h
9)
1Il
Hje
r th
e
aet1
0n
01
the
EI
Cro
nL
ro,
1'J!
.O
eart
hq
uak
e
gro
un
d
mu
tiu
n,
ull
d
lIlI
der
d
std
tio
nary
1'
01 I I
ll.
1111
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IlIo
[lu
n.
Is
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wn
in
F
igs
\0
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d
II,
rl'o
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ectl
vely
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s in
ti
ll!
Cd
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uf
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llct.
d
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uak
e
lll,
th
e
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Ult
s sh
ow
n
In
Fig
s.
10
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II
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ow
ll
idL
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ON
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VA
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SID
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LEV
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FIGU
RE
3.
PLAN
AND
EL
EVAT
IONS
OF
TH
E TE
ST
STRU
CTUR
E [8
)
~
I ,jC
.
,f~
n
s -
E .Q
. 01
DY
NA
MIC
R
ES
PO
NS
E O
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TO
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li
To
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e p
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d
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F sy
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h
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stere
tic ch
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cte
rist
ics
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n in
F
ig.
12
a.
Und
er
the
acti
on
o
f st
ati
on
ary
ra
ndom
ex
rita
tio
n,
the
rela
tiv
e
mo
tio
n w
ith
an
d w
1th
ou
t co
ntr
ol
is
show
n in
F
ig.
12
. A
s in
th
e ca
se o
f li
near
syst
em
s,
it is
cle
ar
that
the
co
ntr
ol
met
hod
is
als
o su
ccess
ful
in
lim
itin
g
the
mo
tio
n
of
this
ty
pic
al
no
nli
near
syst
em.
Co
ncl
usi
on
s
Th
is
pap
er s
how
s th
e fe
asib
ilit
y
of
usi
ng
p
uls
ed
op
en-l
oo
p
ad
ap
tiv
e
co
ntr
ol
for
red
uci
ng
th
e o
scil
lati
on
s o
f ta
ll b
uil
din
gs
on
sim
ilar
dis
tr
ibu
ted
p
aram
eter
sy
stem
s su
bje
cte
d
to
stro
ng
gro
un
d
shak
ing
or
arb
itr
ary
no
ns t
ati
on
ary
d
is t
urb
an
ces.
The
m
etho
d is
o
pen
-lo
op
to
re
du
ce
com
pu
tin
g
tim
e, it
is
ad
ap
tiv
e
in
ord
er
to
tak
e in
to a
cco
un
t th
e va
ryin
~ n
atu
re
of
the
syst
em,
and
it u
ses
pu
lse
co
ntr
ol
to
circ
um
ven
t th
e p
rob
lem
of
pro
du
cin
g
larg
e co
ntr
ol
forc
es
ov
er s
ust
ain
ed
p
erio
ds
of
tim
e.
Red
unda
ncy
tech
niq
ues
u
sin
g
mu
ltip
le
mic
rop
roce
sso
rs
and
mo
tio
n
sen
sors
in
p
ara
llel
wil
l en
sure
v
ery
h
igh
p~obability
for
amp
litu
dt!
an
d ti
min
g co
ntr
ol
of
pu
lse
gen
era
tors
.
Ack
now
ledg
men
t
Th
is
stu
dy
was
su
pp
ort
t!d
in
p
art
by
a g
ran
t w
ith
th
e N
atio
nal
S
cien
ce F
ou
nd
atio
n.
Ref
eren
ces
I.
Haari
, S
.F.
"S
tead
y-S
tate
R
eap
on
se
of
a H
ult
ideg
ue
Sy
stem
wit
h
an
Imp
act
Dam
per
,"
J.
Ap
pU
"d M
uoha
niaa
, V
ol.
4
0,
19
73
, pp
1
27
-13
2.
2.
Ma
sri,
S
.F.
and
Yan
s.
L.
"E
arth
qu
ake
Rt=
:lpon
se.
Sp
ectr
a
of
Syac
e1n8
P
rOV
ided
w
ith
Non
lt
nesr
Au
xil
iary
H
as.
Dam
per.
," P
l'oo.
H
h "'
od
d C
onf.
on
E
arot
hqua
kB
En
yin
ee"i
niJ
, R
ome,
1
97
3.
3.
4.
5.
Nati
on
al
Scie
nce
Fo
un
d.t
ion
(N
SF
).
F"a
.ib
ilit
y o
f F
oro
.. P
ulao
a"
naZ
\lW
rB
[V
I'
t'art
JJ
quak
.. S
imu
lati
on
a,
NSF
G
ran
t PP
R
7)-
15
01
0.
1I •• hi~iton,
DC
: N
SF
, 19
79.
Sa
ffo
rd,
F.B
. an
d
Hat
tri,
S
.F.
uA
na
lyti
cal
and
Ex
per
imen
tal
Stu
die
s o
f a
Mec
ha
nic
al
Pu
loe
Gen
eu
tor,
" A
SM
E J.
En
g.
Ind
.,
Vo
l.
96
, 'S
eri
••
B,
Hay
1
97
4,
pp
45
9-4
70
.
Haad
, 5
.1'.
; B
ekey
, G
.A.;
an
d
Saff
ord
, F
.B.
"Opt
imum
R
esp
on
se
SiD
luia
tio
n o
f H
ult
id
eg
ree
Syo
tellU
l by
P
ulo
. E
xcit
ati
on
,"
ASH
E J.
Dyn
amio
Slid
torn
o,
iofii
laaU
1'O
mon
t, a,
1d
Co
ntr
ol,
V
ol.
9
7,
Serl
••
G,
No.
I,
19
75.
pp
46
-53
.
6.
H..J
.arl
, S
.F.
and
S
aff
ord
. F
.B.
"E
arth
qu
ake
En
viro
nm
ent
Sim
ula
tio
n b
y ·P
ulB
e G~nerator ..
. 11
7th
W
orld
Co
nf.
o
n f
art.
hq'U
lk.
En
ai,
,,,.
rin
g,
lata
nb
ul,
1
98
0.
7.
Ha.r
t,
S.F
.;
Bek
ey,
G .A
.;
and
U
d\J
ad
ta.
F. E
. "O
n-L
ina
Pu
b.
Co
ntr
ol
of
Tall
B
ull
din
ga,"
S
t.'U
otu
l'a
l C
on
tro
l,
ed
. II
.H.E
L
e1
ph
olz
. A
mH
erdu
lU1
No
rth
-Ho
Uan
d
Pu
bU
shln
g'C
".
and
SM
P
ub
licati
on
s,
1980
.
8.
Clo
ug
h,
R.I
I.
and
T
ang
, D
.T.
Ear
thqu
ak ..
Sim
ula
ted
Stu
dy
of
a S
t."l
F''G
m1l
S
tmo
tw·.
, V
ol.
I:
E
xper
im"n
t.:l
l R
dd
ult
a,
E[R
C
75
-6,
Un
lvera
ity
o
f C
ali
forn
ia,
B.r
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Advances in .Dynamic Analysis and Testins
A-49
SP-529
Published by: Society of Automotive Engineers, Inc.
400 Commonwealth Drive Warrendale,PA 15096
October 1982
821459
Pulse Excitation Techniques
ABSTRACT
A series of rectangular or other simple pulses can be convolved with the impulse functions of a structure to induce motions closely approximating those caused by natural and manmade events. ~ Control of the excitation; portability to the site; ease of attachment to the structure; multiaxial excitation; low cost of excitation equipment; and the ability to excite structures from simple harmonic motion to expected multi frequency response-time histories are possible by the development of pulse techniques. Recent investigations have also disclosed the utility of pulse techniques to oppose structural motions as in earthquakes or in large antenna arrays in space.
RECENT ANALYTICAL AND EXPERIMENTAL STUDIES [1)* indicate that a rudimentary series of rectangular or other simple pulses could be convolved with the impulse functions of a structure to induce motions closely approximating those caused by natural and man-made events. This result greatly simplifies the control of high energy devices as the problem is reduced to three functions of ~, off, and amplitude control. It was further determined that the excitation could also be placed directly on structures at one location or at multiple locations of test convenience and in single or multiple axes. When the structural excitation is caused by base motion, pulse simulation with generators attached to the same structure can duplicate the natural or man-made event with the exception of th~ rigid body modes.
Transient shock tests on in-place equipment and buildings to simulate the motions induced by a nuclear event or an earthquake are largely limi ted to single-axis tes t machines. Further
*Numbers in brackets designate references at end of paper.
A-50
F. B. Safford Agbabian Associates
EI Segundo, CA
limitations exist in the size and weight of structures that can be tested. Simulating multiaxis loading on large structures with many degrees of freedom represents a difficul t problem as it is impractical to generate continuously varying forces of sufficient magnitude. On the other hand, short duration forces of large magnitudes over a wide frequency range can be generated by pulse generators. Since a discrete number of pulses superficially presents an appearance quite different from a continuous excitation signal, it becomes necessary to select the pulses in such a way that the resulting vibration of the structure matches as closely as possible the response (e.g., displacement, velocity, or acceleration) produced by the continuous force, as determined by an appropriate error criterion.
Several large energy devices may be adapted for pulse train excitation. These include point source explosives, chemical rockets, metal cutting, and reactance by gas, water, or projectiles. The development and applications of several metal cutting systems are discussed together with a pulse modulated gas reactance system.
The central issue in testing is to induce multiaxial motion-time histories on a structure comparable to those caused by natural or manmade hazards. since failures and malfunctions are essentially nonlinear. Force pulse trains provide practical methods in many applications to test structures and equipments to the thresholds of damage and malfunction by inducing realistic response waveforms.
PROCEDURE
The· procedure to develop the required pulse trains is illustrated in Fig. 1 for a massive nuclear power containment structure or a small equipment rack.. The computational methods are iterative to obtain the pulse train, and the procedure may be used for either linear [2] or nonlinear systems [3]. Various iteration n::ethods may be used; an optimization algorithm [4]
using a spherical random search with a partially automatic control of the variance has proved to be quite efficient. It has been found that the variance can range over ten orders of magnitude, which permits rapid convergence and avoidance of local minima.
It is important to note that the method of Fig. 1 requires that the criterion response to the continuous input be known, which would
(a) Pulse test of nuclear reactor containment structure to simulate earthquake response
SYSTEM R£SPOHS[ (HIGli EXl'tOSIVE FIELD TEST) C~ITERIA
THREAT 'At-AI RSlAST I ~
19Jt~ ~Zl
SPECIFICATIONS
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(b) Pulse test of communications equipment to mat~~ motions induced by air blast loads
FIGURE 1. PROCEDURE FOR PULSE TESTS FOR A w~E RANGE OF STRUCTU~S &~u ENVIRONMENTS
generally not be true in practice. To accom-plish this objective, the approach proposed here assumes that: (1) a mathematical model of the system under study is known, and (2) the inputs of interest (e.g., earthquake or nuclear blast) are given. Under these conditions the "criterion response" can be calculated and used to obtain the pulse train for the simulated test. The structure also can be represented by empirical models derived from mechanical impedance measurements.
The basic criterion used is the integral squared error_ between the reference and simulated response (see Fig. 1), evaluated at a sufficient number of points within the multipledegree-of-freedom system to characterize it as completely as possible. The error criterion is giVen, and then the pulse occurrence times, pulse widths, and the pulse amplitudes are selected by a systematic search algorithm such that the error is minimized.
While the expected motion-time-history response is stressed as above, the pulse units can also be programmed to generate sine aDd random motion responses. These latter motions are useful for measuring impedance and for extracting modal properties of the structure. Additionally, a recent study [5] presented a relatively simple on-line pulse control algorithm suitable for use with distributed par;:,meter systems subjected to nonstationary disturbances. The main feature of the algoritho is that resonance phenomena can be eliminated, or at least drastically reduced, by disorganiZing the orderly and gradual buildup of th~
structural dynamic response by timed firing of a pulse of suitable magnitude applied in the proper direction. Furthermore, in order to minimize the amount of control energy utilized, the control force should be applied only when the structural response exceeds a certain threshold level related to the resistance of the structure.
APPLICATIONS
The 25-story building modeled as a linea::system in Fig. 2, has the mode shapes shown in Fig. 3, and under base excitation by the El Centro Earthquake yields the motion time histories plotted in Fig. 6 (solid line) for the 13th and 23rd floors [6 J . Figure 5 sho",s the driving point impulse functions for Floors 8, 13, 18, and 23 as ",ell as the trans fer impulse functions between flooz:-s and each e=~ci ta tion location. Using the procedures of Figs. 4, 5, and 6, the force pulse trains of Fig. 4 were developed for pulse locations on Floors 8, 13, 18, and 23. The response motions induced by these pulsers are plotted on Fig. 6 (dotted line) and are Virtually identical to the motion~ caused by the El Centro earthquake. Average force required is 50,000 lbf and the average impulse is 17,000 lb-sec. Fifty-two pulses 2n:: required, having average pulse ",idths of 410 ms.
A-51
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18
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PULSE TRAIN
FIGURE 2. PULSERS ARRAYED FOR EARTHQUAKE SIMULATION TEST OF A MULTISTORY BUILDING
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FIGURE 3. BUILDING NATURAL MODES OF VIBRATION
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FIGURE 4. OPTIMUM PULSE TRAINS FOR 25 DOF SYSTEM
FIGURE 5. L'1PULSIVE DISPLACE:ME~IT
RESPONSE TO 25 DOF SYSTEM
FIGURE 6. COMPA.~ISON OF CRITERION AND SL~~TED RESPONS~ OF 25 DOF SYSTEM
A 200,000 lb shock isolated control room (SO ft x 50 ft) for a power plant was tested while functionally operating to induce motiontime histories expected from a specified nuclear base motion threat (7]. One of the four pul se generators used is pictured in Fig. 21. The specified pulse train and the four measured ones are presented in Fig. 7. Typical measured transfer functions of the structure used to calculate the pulse train are presented in Fig. 8 and include transfer function magnitude,
A-52
phase, and impulse function. The predicted control room motion due to base motion hazard is given in Fig. 9 together with comp",ted pulse simulated· motion and motions measured duri~g tests with the pulse generators.
Tests of a large nuclear processing plant were performed to obtain transfer functions and to extract building modes and damping [8]. One of the buildings tested was a reinforced concrete structure 40 ft high, 136 ft wide, and 300 it long (Fig. 10). Figure 11 is a typical
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FIGURE 7. 200,000 LB SHOCK ISOLATED CONTROL ROOM PLATFORM: SPECIFIED AND ACTUAL TEST-INPUT PULSES USING FOUR PULSE GENERATORS
mode shape extracted from the pulse generated data given in Fig. 12. The pulse generator used in these tests is shown in Fib' 23.
Figure l(b) is a schematic for biaxial testing of command, control, and communica tion equipment subjected to battlefield high explosive and nuclear blast loads [9]. Data recorded on a communications equipment rack within the truck shelter during a SOO-ton TNT (equivalent) test is given in Fig. 13. The pulse train required to induce motion in equipment to match the explosive field test data is covered in Fig. 14 with the computed equipment response using the pulse train shown in Fig. 15. The motion of Fig. IS was obtained by convolving the pulse train with the impulse function of the equipment and rack. The impulse function was obtained by inverse transformation of measured impedance functions. This biaxial proj ect is still in progress. Biaxial calibration and development trials of the system pictured in Fig. 24 are displayed in Fig. 16.
The utility of using pulse generators to reduce motions in structures as would be caused by an earthquake has been demonstrated by application to a model three-story steel frame (Fig. 17) that has been extensively studied, both analytically and experimentally [10, 11) at
A-53
the University of California, Berkeley CUeB). A single pulse controller is located on the third floor, and the threshold levels for triggering the controller are set at 0.64 in. relative displacement for the first floor, 0.88 in. for the second floor, and 1 in. for the third floor. Results with and without control are given in Fig. 18. Corresponding results were obtained by locating the pulse controller on either the first or second floors as the response of each mass is kept nearly bounded by the selected threshold levels ..
However, from the control energy point of view, significant reduction in the required impUlse can be achieved i.f the pulse generator is located at the top floor, rather than the lower floor of the structure. The optimum location of pulse generators is being studied as a refinement to conserve impulse requirements. As in the case of EI Centro Earthquake, art.ificial earthquake D1 [12] and stationary random ground motions show similar results that a single controller can effectively control system motion to within any reasonable threshold level.
PULSE GENERATI~G DEVICES
Pulse generating devices developed and now in development are composed of a class of metal cutting systems and a class of gas reactance systems. The metal cutting devices make use of the very high forces required to cut metal [1]. The velocity of the cutting tool and the length of the metal projection govern the pulse duration. For the metal removed, cutting coefficients typically range from 150,000 Ibf/in 3 for aluminum to 300,000 Ibf/in 3 for steeL Metal pulse genera tors prodUCing up to 1,000,000 lbf have been proposed.
Force produced is directly proportional to the volume of metal removed or alternatively to the shear/fracture of chip removal. Waveform is obtained by varying the profile or contour of material to be sheared. Thus, variable forcetime history results· as the depth of cut varies wi th the profile of the metal workpiece. The mos-t efficient means of force production is by use of circular cutting tools similar to broaching operations. Figure 19 provides a schematic of a force profile generator. The shaped nubbins may be spaced as shown or may be continuous over the entire stroke. Figures 2J. through 24 show several machines that are now operable. The biaxial machine (Fig. 24) has been designed to accommodate a third independent test axis should the need arise.
The programmable gas pulse generator showu in Fig. 20 and again in Fig. 25 is undergoing test stand calibrations [13). Two units have been cons tructed and will be mounted in opposition to provide opposing force direction (positive and negative pulse trains). Initial use provides for cold gas, but the system is adaptable for both steam and chemically generated hot gas. Thrust amplitudes are controlled in the on-state by positioning the metering plu6 for flow control. Off-state for the pulse
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FIGURE 8.
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CONTROL ROOM: MEASURED TRANSFER FUNCTION FOR 0.5 Hz TO 500 Hz
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A-54
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FIGURE 9. CONTROL ROOM PLATFORM: ACCELERATION- TIME HISTORIES OF PREDICTED, PULSE-SL~TED, AND PULSE-TESTED MOTIONS
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FREOUENCY. H:z
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FIGURE 12. TYPICAL DATA RECORDS FROM PULSE TRAIN TESTS AND RESULTING TRANSFER (I~~TANCE) FUNCTIONS COMPUTED FROM DATA-PULSE GENERATOR
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FREQUENCY, Hz
MOTION IN EQUIPME}.i TO ~-\TCH EXPLOSr,'E FIELD TEST DATA OF FIG. 13(a)
1000 3000 3500
(b) Fourier codulus of horizontal acceleration response
FIGURE 13. EORIZONiAL RESPO~SE OF CO~NICATIO~S EQUI?HEST FRA.'{E INSIDE SHELTER TO AIR BLAST IN MISERS BLUFF II EVENi
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FIGURE 15. INITIAL COMPUTATION OF PULSE TRAIN GENERATED MOTION IN EQUIPMENT RACK TO MATCH THE OBJECTIVE FUNCTION OF FIG. 13 (a)
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FIGURE 16. INPUT FORCE AND RACK ACCELERATION DATA FROM BIAXIAL TEST
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FIGURE 17. p~~ .~~ ELEVATIONS OF THE TEST STRUCTURE
A-56
S ,. E.Q. ELC LOCATION'" {O, 0, I} Y f = {O. 64, 0.88, 1.0 f -re Td "O.Ol T =0.5 opt
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TIME TIME
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FIGURE 18. RELATIVE DISPLACEMENT RESPO::-;SE UNDER EXCITATION, EL CE~O EARTHQUAKE PULSE CONTROLLER AT THIRD FLOOR
CUTTER END PLATE
30
i 1
(END OF STROKE )
~AAULIC~ HYDRAUL I C CYLINDER NUBBINS, PROFILED FOR
VARYING FORCE REQUIREMENTS
FIGt."RE 19. SC:..,rY_A.TIC OF FORCE PROFILE GE~;ER.HION BY :-STAL CUTTI~IG
A-57
PROGRAI1 S I GHALS ------,
PARALLEL VALVE SYSTEM
TliRUST' ~----
PROGRAI1 S I GHALS 1---------'
SERVO SLAVE VALVE SERVO PILOT VALVE VO I CE [0 I L
FIGURE 20. PROGRk~BLE GAS PULSE GENERATOR COLD GAS SYSTEM -500 TO 10,000 Ibf
FIGURE 21. APPLICATION OF PULSE GENERATOR FOR EQUIPMENT TEST ACCELERATIONTIME HISTORIES (See Figs. 7-9) CAPACITY 8,000 Ibf
FIGURE 22. PULSE GENERATOR USED FOR 'rRA,.'iSFER FUNCTION AND MODE SR~ES OF STRUCTURE, CAPACITI 16,000 ft-lb
A-58
j -
J
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Reproduced best availab
TEST (TRANSMITTER/RECEI
-TEST
FIGURE 23. LARGE PULSE GENERATOR USED TO MEASURE TRANSFER FUNCTIONS AND MODE SHAPES OF LARGE STRUCTURES (See Figs. 10-12) CAPACITY 54,000 ft-lb
FIGURE 24. BIAXIAL PULSE GENERATOR TRANSIENT SHOCK TESTS OF EQUIPMENT DUPLICATING ENVIRONMENTAL ACCELERATION-TIME HISTORIES (See Figs. 13-16) CAPACITY 15,000 Ibf EACH AXIS
A-59
~eproduced from est available COpy,
FIGURE 25. GAS PULSE GENERATOR USED FOR STRUCTURE TESTS ACCELERATION-TIME HISTORIES, FOR TRANSFER FUNCTIONS AND MODE SHAPES, AND FOR SUPPRESSION OF STRUCTURAL MOTIONS (See Figs. 17,18)
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INPUT VOLTAGE ~O~UT '/ CONTROL SIGNAL
10,000 FJRCE
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120 msec: I
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FIGURE 26. TYPICAL FORCE PROFILE OF GAS PULSE GE~~RATOR
occurs by signaling the hydraulic actuator to move the metering plug to seal off gas flow at the nozzle. Two devices will be used for earthquake and anti-earthquake investigations on the structure at the University of California, Berkeley (Fig. 17). Typical performance characteristics of the gas pulser is shown in Fig. 26. Using peaking methods superimposed on the control signal input, rise times of 11 ms have been obtained. The system has also been designed to accommodate two 90 gpm 'Jalves for parallel operation. This configuration will yield rise times of 7 ms.
CONCLUSIONS
The use of force pulse trains to induce structural motions simulating the effects of natural and man-made events has been introduced to circumvent the problem of producing large control forces over sustained periods of time. Additionally, the use of pulsed adaptive control for reducing oscillations of large structures to unknown disturbances has been shown to be feasible.
A number of metal cutting pulse generators have been produced and placed in operation to induce large structural motions of transient shock characteristics and also to measure the modal characteristic and impedance of structures. These devices are attractive due to low cost., portability, and ease of control. Pulse forces from a few hundred pounds to a million pounds are possible with frequency content variable up to recorded motions of 5000 Hz.
Programmable gas pulsers have also been developed and are now under test. Gas, hydraulic, and explosive source pulsers are being investigated for applications requiring inertial references.
ACKNOWLEDGEMENTS
7he gas pulse system and the on-line motion suppression study was supported in part by a grant from the National Science Foundation under t.he direction of Dr. John B. Scalzi. fhe mechanical pulse generators- were developed through the support of Hr. C.C. Huang, Corps of Engineers, Mr. R.E. Walker, Waterways Experiment Station, and Dr. William Schuman, Ballistic Research Laboratory. In addition to the staff of Agbabian Associates, Professors S.F. Masri and G.A. Bekey of the University of Southern California provided major contributions in control algorithms.
REFERENCES
1.
2.
!\-61
Safford, F.B. and Masri, S.F. "Analytical and Experimental Studies of a Mechanical Pulse Generator," Jal of Ea~. for Industrv. ASME, Series B, 96:2, May 1974, pp. 459-470
Masri, S.F. and Safford, F.B. ·'Dyn.3oic Environment Simulation by Pulse Techniques," Proc. ASCE Eng. Mech. Div. 10J.:E:~1,
Feb 1976, pp. 151-169.
3.
4.
S.
6.
7.
Masri, S.F. and Caughey, T.N. "A Nonparametric Identification Technique for Nonlinear Dynamic Problems, n Jnl of Appl. Mech. ASME, 46:2, Jun 1979.
Masri, S.F.; Bekey, G.A.; and Safford, F.B. "An Adaptive Random Search Method for Identification of Large Scale Nonlinear Systems," 4t.h Symp. for Identification and System Parameter Estimation, Int. Federation of Aut.omatic Control, Tbilisi, USSR, Sep 1976.
Masri, S.F.; Bekey, G.A.; Safford, LB.; and Dehghanyar, T.J. "Anti-Earthquake Application of Pulse Generat.ors," Proc. Dynamic Response of Structures, Instrumentation, Testing Methods and System Identifica tion, ASCE Special ty Conference, Atlanta, GA, Jan 1981.
Masri, S.F. and Safford, F.B. "Earthquake Environment Simulation by Pulse Generators;' Proc. 7th World Conf. on Earthquake Eng. Istanbul, Turkey, Sep 8-13, 1980.
Safford, F.B. et al. ~Air-Blast and Ground Shock Simulation Testing of Massive Equipment by Pulse Techniques, Sth Int. Symp. on Military Application of Blast Simulation, Fortifikationsforvaltningen, Stockholm, Sweden, May 23-26, 1977.
8.
9.
10.
11.
12.
Yates, D.G. and Safford, F.B. "Measurement of Dynamic Structural Characteristics of Massive Buildings by High-Level Multiple Techniques," Shock £. Vibration Bull., 50, SVIC. Washington, DC: Naval Res. Lab, 1980.
Safford, F.B. et al. "Biaxial Accelleration Simulation Test Machine," Proc. 7th Int. Symp. on Military Application of Blast Simulation, Medicine Hat, Alberta, Canada, Jul 1981. .
Cough, R.W. and Tang, D.T. "Earthquake Simulated Study of a Steel Frame Structure, Vol. I: Experimenta I Results," EERC 75-6, Univ. of California, Berkeley, Apr 1975.
Tang, D.T. "Earthquake Simulated a Steel Frame St.ructure, Vol. II: cal Results," EERC 75-36, Univ •. fornia, Berkeley, Oct 1975.
Study of Analyti- -of Cali-
Jennings, Tsai, N.C. California 1968.
P.C.; Housner, G.W.; and "Simulated Earthquake ~otions," Institute of Technology Report,
13. Safford, F.B. Validation of Pulse Techniques for the Environmental Simulation of Earthquake Motions in Civil Structures, U.S. National Science Foundation Grant No. PFR77-15010, Washington, D.C., 1978.
