response to classical pulse excitation
DESCRIPTION
Unit 23. Response to Classical Pulse Excitation. Classical Pulse Introduction . Vehicles, packages, avionics components and other systems may be subjected to base input shock pulses in the field The components must be designed and tested accordingly - PowerPoint PPT PresentationTRANSCRIPT
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Response to Classical Pulse Excitation
Unit 23
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Classical Pulse Introduction
Vehicles, packages, avionics components and other systems may be subjected to base input shock pulses in the field
The components must be designed and tested accordingly
This units covers classical pulses which include:
Half-sine Sawtooth Rectangular etc
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Shock Test Machine
Classical pulse shock testing has traditionally been performed on a drop tower
The component is mounted on a platform which is raised to a certain height
The platform is then released and travels downward to the base
The base has pneumatic pistons to control the impact of the platform against the base
In addition, the platform and base both have cushions for the model shown
The pulse type, amplitude, and duration are determined by the initial height, cushions, and the pressure in the pistons
platform
base
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Half-sine Base Input
1 G, 1 sec HALF-SINE PULSE
Time (sec)
Accel (G)
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Natural Frequencies (Hz):
0.063 0.125 0.25 0.50 1.0 2.0 4.0
Systems at Rest
Soft Hard
Each system has an amplification factor of Q=10
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Click to begin animation. Then wait.
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Natural Frequencies (Hz):
0.063 0.125 0.25 0.50 1.0 2.0 4.0
Systems at Rest
Soft Hard
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Responses at Peak Base Input
Soft Hard
Hard system has low spring relative deflection, and its mass tracks the input with near unity gain
Soft system has high spring relative deflection, but its mass remains nearly stationary
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Soft Hard
Responses Near End of Base Input
Middle system has high deflection for both mass and spring
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Soft Mounted Systems
Soft System Examples:
Automobiles isolated via shock absorbers
Avionics components mounted via isolators
It is usually a good idea to mount systems via soft springs.
But the springs must be able to withstand the relative displacement without bottoming-out.
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Isolator Bushing
Isolated avionics component, SCUD-B missile.
Public display in Huntsville, Alabama, May 15, 2010
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But some systems must be hardmounted
Consider a C-band transponder or telemetry transmitter that generates heat
It may be hardmounted to a metallic bulkhead which acts as a heat sink
Other components must be hardmounted in order to maintain optical or mechanical alignment
Some components like hard drives have servo-control systems, and hardmounting may be necessary for proper operation
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SDOF System
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Free Body Diagram
Summation of forces in the vertical direction
)x(yk)xy(cxm
kzzc)yzm(
ymkzzczm
y(k/m)zz(c/m)z
xmF
Let z = x - y. The variable z is thus the relative displacement.
Substituting the relative displacement yields
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Derivation
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By convention,
nωξ 2c/m
2nωk/m
yz2nωznω2ξz
Substituting the convention terms into equation,
is the natural frequency (rad/sec)
is the damping ratio
nω
This is a second-order, linear, non-homogenous, ordinary differential equation with constant coefficients.
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Derivation (cont.)
yz2nωznω2ξz
Solve for the relative displacement z using Laplace transforms.
Then, the absolute acceleration is
yzx
Tt,0
Tt0,TtsinA
)t(y
For a half-sine pulse
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SDOF Example
A spring-mass system is subjected to:
10 G, 0.010 sec, half-sine base input
The natural frequency is an independent variable
The amplification factor is Q=10
Will the peak response be
> 10 G, = 10 G, or < 10 G ?
Will the peak response occur during the input pulse or afterward?
Calculate the time history response for natural frequencies = 10, 80, 500 Hz
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SDOF Response to Half-Sine Base Input
>> vibrationdata > Miscellaneous > Shock > SDOF Response: Classical Base Input > Time History Response
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maximum acceleration = 3.69 G minimum acceleration = -3.15 G
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maximum acceleration = 16.51 G minimum acceleration = -13.18 G
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maximum acceleration = 10.43 G minimum acceleration = -1.129 G
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Summary of Three Cases
Natural Frequency (Hz)
Peak PositiveAccel (G)
Peak Negative Accel (G)
10 3.69 3.15
80 16.5 13.2
500 10.4 1.1
A spring-mass system is subjected to:
10 G, 0.010 sec, half-sine base input
Shock Response Spectrum Q=10
Note that the Peak Negative is in terms of absolute value.
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Half-Sine Pulse SRS
>> vibrationdata > Miscellaneous > Shock > SDOF Response: Classical Base Input > Shock Response Spectrum
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X: 80 HzY: 16.51 G
SRS Q=10 10 G, 0.01 sec Half-sine Base Input
Natural Frequency (Hz)
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Homework
Repeat the examples for the half-sine pulse
Also, do this for a 10 G, 10 msec terminal sawtooth pulse