vibrations of machine foundationsszepesr/anyagok/oktatas/ngb-se005_4/eloadas/gepalap… ·...
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Vibrations of
Machine Foundations
Richard P. Ray, Ph.D., P.E.Civil and Environmental Engineering
University of South Carolina
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ATST Telescope and FE Model
Fundamentals-Modeling-Properties-Performance
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Summary and Conclusions (Cho, 2005)1.
High fidelity FE models were created2.
Relative mirror motions from zenith to horizon pointing: about 400 μm in translation and 60 μrad in rotation.
3.
Natural frequency changes by 2 Hz as height changes by 10m.4.
Wind buffeting effects caused by dynamic portion (fluctuation) of wind 5.
Modal responses sensitive to stiffness of bearings and drive disks
6.
Soil characteristics were the dominant influences in modal (dynamic) behavior of the telescopes.
7.
Fundamental Frequency (for a lowest soil stiffness):OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz
8.
A seismic analysis was made with a sample PSD9.
ATST structure assembly is adequately designed:1.
Capable of supporting the OSS2.
Dynamically stiff enough to hold the optics stable3.
Not significantly vulnerable to wind loadings
Fundamentals-Modeling-Properties-Performance
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Topics for Today
FundamentalsModelingPropertiesPerformance
AlapokModellezésTulajdonságokGyakorlati Alkalmazás
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Foundation Movement Alapok Mozgáslehetőségei
X
ZY
θ
ψ
φ
Fundamentals-Modeling-Properties-Performance
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Design Questions (1/4) Tervezés
How Does It Fail?Static SettlementDynamic Motion Too Large (0.02 mm)Settlements Caused By Dynamic MotionLiquefactionWhat Are Maximum Values of Failure? (Acceleration, Velocity, Displacement)
Hogy rongálódik/megy tönkre?
Statikus süllyedésDinamikus mozgás túl nagy (0,02 mm)Süllyedés dinamikus mozgás következtébenMegfolyósodásRongálódás maximális értékei (gyorsulás, sebesség, eltolódás)
Fundamentals-Modeling-Properties-Design-Performance
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Velocity Requirements Sebesség Követelmények
Massarch
(2004) "Mitigation of Traffic-Induced Ground Vibrations"
Fundamentals-Modeling-Properties-Performance
0,40
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300 800
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Design Questions
(2/4) Tervezés
What Are Relations Between Loads And Failure Quantities?
Loads -Harmonic, Periodic, RandomLoad→ Structure →Foundation → Soil →Neighboring StructuresModel: Deterministic or Probabilistic
Mi a kapcsolat terhelési és törési mennyiségek között?Terhelések- Harmónikus, Periódikus, VéletlenszerüTerhelés → Épület →Alapozás → Talaj → KözeliÉpületekModel: Determinisztikus és probabilisztikus
Fundamentals-Modeling-Properties-Performance
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Harmónikus
Periódikus
Véletlenszerű
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Design Questions (3/4) Tervezés
Hogy határozzuk meg a tervezéshez szükséges paramétereket? (How do we measure what is necessary?)
Teljes méretarányú teszt (Full scale Test)Prototípus teszt (Prototype Test)Kis méretű teszt (Small Scale Tests (Centrifuge))Laboratóriumi teszt (Laboratory Tests (Specific Parameters))Számítógépes program (Computer Model)
Fundamentals-Modeling-Properties-Performance
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Design Questions (4/4)Milyen biztonsági tényezőt használjunk? (What Factor of Safety Do We Use? )
Van a biztonsági tényezőnek értelme? (Does FOS Have Meaning)Mi történik törés után (What Happens After There Is Failure)
Életvesztés (Loss of Life)Tulajdonvesztéd (Loss of Property)Gyártás kihagyás (Loss of Production)
Mi a munka célja, tervezett élettartalma, értéke (Purpose of Project, Design Life, Value)
Fundamentals-Modeling-Properties-Performance
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r -2 r -2 r -0.5
r -1
r -1
r
Nyíróhullám
Vertical component
Horizontal component
Shear window
Rayleigh wave
Relative amplitude+
+
+
+
- -
+
+
Wave TypeHullám típus
Összes energia százaléka
Rayleigh 67Shear 26
Compression 7
Waves
Fundamentals-Modeling-Properties-Performance
Compresszió
hullámNyíró ablak
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Alapok Modellezése (Modeling Foundations)
Egyesített Tömb (m,c,k)Lumped Parameter (m,c,k) Block System
Parameters Constant, Layers, Special Ellenállási Függvények Impedance Functions
Function of Frequency (ω), LayersPeremérték Feladatok Boundary Elements (BEM)
Infinite Boundary, Interactions, LayersVéges Elemes (Finite Element/Hybrid (FEM, FEM-BEM))
Complex Geometry, Non-linear Soil
Fundamentals-Modeling-Properties-Performance
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Lumped Parameter
(Egyesített tömb))sin( tPP o ω=
m
Gk
m
cν ρ
)sin(0 tPkzzczm ω=++ &&&
r
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Egy szabadságfokú (Single Degree of Freedom)
)()(
)(
)()(
0
2
NormmNForceSpringzk
Norsecm
msecNForceDampingzc
NorsecmkgForceInertiazm
zkzczm
z
z
z
zzz
⎟⎠⎞
⎜⎝⎛=
⎟⎠⎞
⎜⎝⎛⎟⎠⎞
⎜⎝⎛ −
=
⎟⎠⎞
⎜⎝⎛=
=++
&
&&
&&&
k
m
c
z
Tehetetlenségi erő
Rugó erő
Csillapító Erő
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Egy szabadságfokú Single Degree of Freedom
condependssforsolution
smcsthen
mksetandembydivide
ekcsmswhereconstantezformtakewillsolution
zkzczm
n
nst
st
stzzz
0
0)(.......
0
22
2
2
=++
=
=++
==
=++
ω
ωα
α
αα
&&&
c=0…Undamped
c=2mω…Critically
Damped
c<2mω…Underdamped
osztás
megoldás állandó
ahol
tehát
s megoldása c-től függ
Nem csillapított
Alul csillapított
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Single Degree of Freedom
)cos()0()sin()0()(
)0()0(
)(,)cos()sin()()sin()cos('
.).(,)(
...0
2121
22
tztztz
AzandBz
conditioninitialfBAtBtAtztiteidentitysEuler
condinitfwhereeetz
issmcs
nnn
n
n
nnti
titi
nn
n
nn
ωωω
ω
ωωωω
αααα
ωω
ω
ωω
+⎟⎟⎠
⎞⎜⎜⎝
⎛=
==
=+=+=
=+=
±==++
−
&
&
undamped
)0(z&
z(0)t
Kiinduló feltétel
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[ ] tn
t
nncrit
n
n
n
n
etztztz
condinitfwhereettzmcsandmccthenif
mc
mcsthen
presentdampingifsmcs
ω
ω
ω
αααα
ωω
ω
ω
−
−
++=
=+=
−=−====
−⎟⎠⎞
⎜⎝⎛±−=
=++
)0()1)(0()(
.).(,)()(2
20
22
0
2121
22
22
&
critical
Single Degree of Freedom
z(0)
)0(z&
t
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( )( )
⎥⎦
⎤⎢⎣
⎡+
+=
+=
+=+=
±−=−±−=
−===
<<
−
−
−−−−+−
)cos()0()sin()0()0()(
)cos()sin(()(
)(
1
02
2121
22
2
tztDzzetz
tBtAetz
eeeeetz
iDDDsthen
DandratiodampingccDsuppose
thenmcif
DDD
ntD
DDtD
tititDtitDtitD
Dnnnn
nDcrit
n
n
n
DDnDnDn
ωωω
ω
ωω
αααα
ωωωωω
ωω
ω
ω
ω
ωωωωωωω
&
dunderdampe
Single Degree of Freedom
See Chart
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Single Degree of Freedom)sin(0 tPzkzczm Pzzz ω=++ &&&
k
m
c
)sin( tPP Po ω=
( ) ( ){ }
( )( )
22
2222
0
1
2tan
sin
cos)sin(
⎟⎠⎞⎜
⎝⎛−
⎟⎠⎞⎜
⎝⎛
=−
=
−+−
+
+= −
n
P
n
P
P
P
P
PP
DDDt
D
mkc
tcmk
PtBtAez n
ωω
ωω
ωωφ
φωωω
ωωω
critccD =
mk
n =ω 21 DnD −=ωωkmccrit 2=
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SDOF Átmenti és Állandó Transient
and Steady-State
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( )( )
222
0max
2222
0
21
1
sin)(
⎥⎦
⎤⎢⎣
⎡+
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
=
−+−
=
n
P
n
P
P
PP
DkPz
tcmk
Ptz
ωω
ωω
φωωω
222
21
1
⎥⎦
⎤⎢⎣
⎡+
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
=
n
P
n
P
staticmax
D
zz
ωω
ωω
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USCUSCUSCFundamentals-Modeling-Properties-Performance
Dynamic Magnification (Logarithmic)
0.1
1
10
100
0.1 1 10Frequency Ratio (ωP/ωn)
Mag
nific
atio
n
D=0.02D=0.05D=0.10D=0.20D=0.50
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Lumped Parameter System
Kx
Z
ψ
KzCz
Cx
KψCψ
/2 Cψ
/2
X
)sin(0 tPzkzczm Pzzz ω=++ &&&
mIψ
Fundamentals-Modeling-Properties-Performance
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Rendszer paraméterek Lumped Parameter Values
Mode Vertical
zHorizontal
x Rocking
ψTorsion
θ
Stiffness k
Mass Ratio m
Damping Ratio, D
ν−14Gr
ν−28Gr
)1(38 3
ν−Gr
316 3Gr
5rIρθ
38)2(
rm
ρν−
34)1(
rm
ρν−
2/1ˆ425.0
m 2/1ˆ288.0
m 2/1ˆ)ˆ1(15.0
mm+ m̂2150.0
+
m̂
D=c/ccr
G=Shear Modulus ν=Poisson's Ratio r=Radius ρ=Mass Density Iψ
,Iθ
=Mass Moment of Inertia
58)1(3
rIρ
νψ −
Fundamentals-Modeling-Properties-Performance
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Design Example 1
(Példa)VERTICAL COMPRESSORUnbalanced Forces
(kiegyensúlyozatlan erők)•Vertical = 45 kN•Horizontal
Primary = 0,5 kN•Operating Speed
= 450 rpm•Wt Machine + Motor = 5 000 kg
Soil PropertiesShear Wave Velocity Vs
= 250 m/secDensity, ρ
= 1600 kg/m3
Shear Modulus, G = 1,0e8 PaPoisson's Ratio, ν
= 0,33
DESIGN CRITERION:Smooth Operation At SpeedVelocity <0,10 in/sec Displacement < 0,002 in <0,05mm
Jump to Chart
Fundamentals-Modeling-Properties-Performance
függőlegesvízszintesüzemelő seb.
Gép+motor súlya
Talaj jellemzőkTervezési feltétel
Nyíró hullám
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rGrQmm
kQZ
zstatic ×××
=−
=== 800
100,141000)00045(667,0
4)1(05,0 ν
mr 5.105.0
075.0==
( )
mmZZD
Mm
D
mr
m
staticdynamic
z
05,0210,153,0
ˆ425,0
65,055,1160040002367,0
4)1(ˆ 33
==
⎟⎠⎞
⎜⎝⎛≈==
=×
×=
−=
ρν
Try a 3 x 2,5 x 1 foundation block, r = 1,55 m
Mass = 18 000 kg Total Mass = 18 000 + 5 000 = 23 000 kg
Jump to Figure
Fundamentals-Modeling-Properties-Performance
667,0100,14
)1(4 8 rGrk ×××
=−
=ν
34)1(ˆ
rmm
ρν−
=tömeg
tömbalaptest
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Design Example -
Table Top5m
10m5m
4m
Q0
=1800 N
ψ
m=250 000 kg
Iψ
=1,0 x 107
N-m-sec2
Soil PropertiesShear Wave Velocity Vs
= 200 m/secShear Modulus, G = 6,80x107
PaDensity, γ
= 1700 kg/m3
Poisson's Ratio, ν
= 0,33
DESIGN CRITERION
5.0 mm/sec Horizontal Motion at Machine Centerline
X = 0,04 mm from combined rocking and sliding
Speed = 320 rpm
Slower speeds, X can be larger
Fundamentals-Modeling-Properties-Performance
X
Emelt (asztal) alap
sebesség
Kisebb sebességnél, x megnőhet
együttes rocking, csúszás
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USCUSCUSC
Horizontal Translation Only
mmkQXMag
mD
rmmmlwrtEquivanlen
xstaticx
37
02/1
3
103,199,3108,6
33,028
18002,141,0ˆ288,0
49,08
2ˆ99,3510
−×=××
−==≈∴==
=−
==×
==ρ
νππ
Rocking About Point "O"
0,25019,029,3)29,31(
15,0ˆ)ˆ1(
15,0
29,3)39,3(1700
100,18
)67,0(38
)1(3ˆ
/4,32100,110054,1
/10054,1)33,01(3
39,31080,68)1(3
8
/5,3332039,33
5103
5
7
5
7
10
10373
43
43
=∴=+
=+
=
=×
=−
=
=××
==
×=−
×××=
−=
===×
==
ψψψ
ψ
ψψ
ψ
ψ
ψ
ρν
ω
ν
ωππ
Magmm
D
rI
m
secradIk
radNGrk
secradrpmmlwrEquivalent
n
Fundamentals-Modeling-Properties-Performance
Ax = 40x10-3
mm
csak vízszintes mozgás
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USCUSCUSC
mmResonanceAt
mmhXMotionHorizontal
radkMDeflectionAngularStatic
mNMBaseAboutMomentStatic
s
os
33
37
710
0
100,85)104,3(0,25
104,341054.8
1054.810054.1
9000900051800
−−
−−
−
×=×=
×=××=×==
×=×
===
−=×==
ψ
ψ
ψ
ψ
Fundamentals-Modeling-Properties-Performance
ψ
X
X = 40x10-3
mm
Dynamic Magnification (Linear)
0
5
10
15
20
25
30
0,0 0,5 1,0 1,5 2,0Frequency Ratio (ωP/ωn)
Mag
nific
atio
n
0,02
0,05
0,1
0,2
0,5
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USCUSCUSC
Impedance Methods
Based on Elasto-Dynamic SolutionsCompute Frequency-Dependent Impedance Values (Complex-Valued)Solved By Boundary Integral Methods Require Uniform, Single Layer or Special Soil Property Distribution Solved For Many Foundation Types
Fundamentals-Modeling-Properties-Performance
Ellenállási függvények
Frekvenciától függő ellenállási értékek
Peremérték integrál módszer
Egyenletes, egy réteg, speciális talajérték eloszlás szükséges
Többfajta alap típusra megoldott
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USCUSCUSC
Impedance Functions
( ))sin()cos( titPePP oti
o ωωω +==
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛++×=+== SOILSTATIC
z
zz DKCikKCiK
ARS
ωωωω 2)(
Radiation DampingSoil Damping
Jump Wave
Sz
Fundamentals-Modeling-Properties-Performance
Energia csillapítás Talaj csillapítás
![Page 36: Vibrations of Machine Foundationsszepesr/anyagok/oktatas/NGB-se005_4/eloadas/gepalap… · Vibrations of Machine Foundations Richard P. Ray, Ph.D., P.E. Civil and Environmental Engineering](https://reader034.vdocuments.mx/reader034/viewer/2022051719/5a72a27e7f8b9ab1538da7d2/html5/thumbnails/36.jpg)
USCUSCUSC
Impedance Functions
Luco
and Westmann
(1970)
sVr
Gra ωρω ==0
Fundamentals-Modeling-Properties-Performance
ψ
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USCUSCUSC
Impedance Functions
Fundamentals-Modeling-Properties-Performance
ψ
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USCUSCUSC
Boundary Element
Stehmeyer
and Rizos, 2006
Fundamentals-Modeling-Properties-Performance
Peremérték feladatok
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USCUSCUSC
B-Spline
Impulse Response Approach
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
[ ]{ } [ ]{ } { } tie ωpuKuM =+&&
Fundamentals-Modeling-Properties-Performance
{ } { }[ ] [ ]{ }{ } { }pUMK
Uu=−
=2ω
ω thene ti
![Page 41: Vibrations of Machine Foundationsszepesr/anyagok/oktatas/NGB-se005_4/eloadas/gepalap… · Vibrations of Machine Foundations Richard P. Ray, Ph.D., P.E. Civil and Environmental Engineering](https://reader034.vdocuments.mx/reader034/viewer/2022051719/5a72a27e7f8b9ab1538da7d2/html5/thumbnails/41.jpg)
USCUSCUSCFundamentals-Modeling-Properties-Performance
G1
,ρ1
,ν1
u1
u2
u7
u8
[ ] ),,( 1111 νρGfnK =
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
8
7
2
1
8,87,82,81,8
8,77,72,71,7
8,27,22,21,2
8,17,12,11,1
uu
uu
kkkkkkkk
kkkkkkkk
[ ] )( 11 ρfnm =
linearlinear
dcxyybxau iii
==
+++=
σε
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USCUSCUSC
[ ]{ } [ ]{ } { } tie ωpuKuM =+&&
tie
ppppp
uuuuu
kkkkkkkkkkkk
kkkkkkk
uuuuu
mm
mm
m
ω
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
=
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
+
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
5
4
3
2
1
5
4
3
2
1
5,54,53,5
5,44,43,42,4
5,34,33,32,31,3
4,23,22,21,2
3,12,11,1
5
4
3
2
1
5
4
3
2
1
&&
&&
&&
&&
&&
{ } { } { } { }[ ] [ ]{ }{ } { } { }[ ] { } valuedcomplexare
forsolvegivenandethenezif titi
−=−
−==
ZKZpZMK
ZzZ
,,2
2
ωω
ω ωω &&
( )22 1221* DiDDGG −+−=
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USCUSCUSC
Dynamic p-y
Curves
Tahghighi
and Tonagi
2007
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Soil PropertiesShear Modulus, G and Damping Ratio, D
Soil TypeConfining StressVoid RatioStrain Level
Field: Cross-Hole, Down-Hole, Surface Analysis of Seismic Waves SASWLaboratory: Resonant Column, TorsionalSimple Shear, Bender Elements
Fundamentals-Modeling-Properties-Performance
Talaj jellemzők
Hézagtényező
Talajtípus
Nyúlás szint
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USCUSCUSC
Crosshole TestingOscilloscope
PVC-cased Borehole
PVC-cased Borehole
DownholeHammer(Source) Velocity
Transducer(GeophoneReceiver)
Δt
Δx
Shear Wave Velocity:Vs
= Δx/Δt
TestDepth
ASTM D 4428
Pump
packer
Note: Verticality of casingmust be established by
slope inclinometers to correctdistances Δx with depth.
SlopeInclinometer
SlopeInclinometer
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USCUSCUSC
Resonant Column Test
G, D for Different γ
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Torsional
Shear Test
Schematic Stress-Strain
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Hollow Cylinder RC-TOSS
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
TOSS Test Results
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Steam Turbine-Generator (Moreschi
and Farzam, 2003)
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Machine Foundation Design Criteria
Deflection criteria: maintain turbine-generator alignment during machine operating conditions
Dynamic criteria: ensure that no resonance condition is encountered during machine operating conditions
Strength criteria: reinforced concrete design
Fundamentals-Modeling-Properties-Performance
Jump to Resonance
El/kihajlási kritérium: a turbina-generátor szintben maradjon működése alatt
Dinamikus feltétel: nincs rezonancia a gép működése alatt
Erősségi feltétel: előfeszített beton tervezés
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USCUSCUSC
STG Pedestal Structure
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Vibration Properties Evaluation
Identification of the foundation natural frequencies for the dominant modesFrequency exclusion zones for the natural frequencies of the foundation system and individual structural members (±20%)Eigenvalue analysis: natural frequencies, mode shapes, and mass participation factors
Fundamentals-Modeling-Properties-Performance
Az alap saját frekvenciáinak meghatározása a domináns lengésekre/módokra
Kihagyási frekvencia zónák a természetes frekvenciákra
Eigenérték
elemzés:természetes frekvenciák, lengésmódnál alakok, tömeg együttdolgozása
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USCUSCUSC
XYZ
XYZ
Finite Element Model Structure and Base
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Low Frequency Modes
1st
mode
6.5 Hz95 % m.p.f.
2nd
mode
7.2 Hz76 % m.p.f
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
High Frequency Modes
28th
mode
46.3 Hz0.3% m.p.f
42nd
mode
64.6 Hz0.03% m.p.f
Excitation frequency: 50-60 HzFundamentals-Modeling-Properties-Performance
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USCUSCUSC
Local Vibration Modes
Identification of natural frequencies for individual structural members
Quantification of changes on vibration properties due to foundation modifications
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
ATST Telescope and FE Model
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Optics Lab mass/Instrument weight = 228 tonsWind mean force = 75 N, RMS = 89 N Ground base excitation PSD = 0.004 g2/hzConcrete Pier
High Strength Concrete (E=3.1×1010 N/m2, ν=0.15)
Soil Stiffness, kFour different values using Arya & O’Neil’s formula based on the site test data (Shear modulus:30~75ksi, Poisson’s ratio:0.35~0.45)
Assumptions in FE analyses
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
•
Soil property range: Shear modulus (30~75ksi), Poisson’s ratio (0.35~0.45)•
Pier Footing: Diameter (23.3m)•
“min”
for shear modulus of 30 ksi; “max”
for 75 ksi
Frequency vs
Soil Stiffness
Stiffness min min+33.3% min+66.6% maxKx 1.19E+10 1.83E+10 2.48E+10 3.12E+10Ky 1.19E+10 1.83E+10 2.48E+10 3.12E+10Kz 1.48E+10 2.45E+10 3.41E+10 4.38E+10Krx 1.34E+12 2.21E+12 3.09E+12 3.96E+12Kry 1.34E+12 2.21E+12 3.09E+12 3.96E+12Krz 1.74E+12 2.61E+12 3.49E+12 4.36E+12
6.3 7.0 7.4 7.56.4 7.1 7.5 7.79.4 9.7 9.9 109.4 10.3 11.1 11.810.4 11.9 12.6 13.311.2 13.0 13.6 13.7
456
MODE123
Stiffness units = SI, frequency mode (hz)
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Summary and Conclusions (Cho, 2005)1.
High fidelity FE models were created2.
Relative mirror motions from zenith to horizon pointing: about 400 μm in translation and 60 μrad in rotation.
3.
Natural frequency changes by 2 hz
as height changes by 10m.4.
Wind buffeting effects caused by dynamic portion (fluctuation) of wind 5.
Modal responses sensitive to stiffness of bearings and drive disks6. Soil characteristics were the dominant influences in modal
behavior of the telescopes.7.
Fundamental Frequency (for a lowest soil stiffness):OSS=20.5hz; OSS+base=9.9hz; SS+base+Coude+soil=6.3hz
8.
A seismic analysis was made with a sample PSD9.
ATST structure assembly is adequately designed:1.
Capable of supporting the OSS2.
Dynamically stiff enough to hold the optics stable3.
Not significantly vulnerable to wind loadings
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Free-Field Analytical Solutions
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−=
RVz C
rHaRVLiru ωρβ
ωθ 2003
0 )(2
)0,,(
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
RVr C
rHaRVMiru ωρβ
ωθ 2103
0 )(2
)0,,(
uruz
Fundamentals-Modeling-Properties-Performance
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USCUSCUSCFundamentals-Modeling-Properties-Performance
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USCUSCUSCFundamentals-Modeling-Properties-Performance
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USCUSCUSCFundamentals-Modeling-Properties-Performance
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USCUSCUSCFundamentals-Modeling-Properties-Performance
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USCUSCUSCFundamentals-Modeling-Properties-Performance
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USCUSCUSC
Karlstrom
and Bostrom
2007
Trench Isolation
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Chehab
and Nagger 2003
Fundamentals-Modeling-Properties-Performance
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USCUSCUSC
Celibi
et al (in press)
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USCUSCUSC
Thank-you
Questions?
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USCUSCUSC
r -2 r -2 r -0.5
r -1
r -1
r
Shear wave
Vertical component
Horizontal component
Shear window
Rayleigh wave
Relative amplitude+
+
+
+
- -
+
+
Wave Type Percentage of Total Energy
Rayleigh 67Shear 26
Compression 7
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USCUSCUSC
Waves
Rayleigh, R Surface
Shear,S Secondary
Compression, P Primary
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USCUSCUSC
Machine Performance ChartPerformance Zones
A=No Faults, New
B=Minor Faults, Good Condition
C = Faulty, Correct In 10 Days To Save $$
D = Failure Is Near, Correct In 2 Days
E = Stop Now
0.002
450