Shock Response Spectrum

Welcome to Vibrationdata Pyrotechnic Shock &
Shock Response Spectrum Page


 

http://www.vibrationdata.com/Resources/LinearShapeCharge.jpg
 Figure 1.  Launch Vehicle Stage Separation Test
The source device is linear shaped charge.
 INTRODUCTION

Mechanical shock pulses are often analyzed in terms of shock response spectra. The shock response spectrum assumes that the shock pulse is applied as a common base input to an array of independent single-degree-of-freedom systems. The shock response spectrum gives the peak response of each system with respect to the natural frequency. Damping is typically fixed at a constant value, such as 5%, which is equivalent to an amplification factor of Q=10.

The shock response spectrum is particularly suited for analyzing pyrotechnic shock. It may also be used for evaluating classical pulses, such as a half-sine pulse.
This page offers tutorials which explain the shock response spectrum, as well as software tools for implementing this function.
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SRS Algorithm

Introduction to the Shock Response Spectrum:    srs_intr.pdf
A digital recursive filtering relationship is developed from the convolution integral.
Derivation of the Filter Coefficients for the Ramp Invariant Method as Applied to Base Excitation of a Single-degree-of-Freedom System: ramp_invariant_base.pdf
K. Ahlin, Shock Response Spectrum Calculation - An Improvement of the Smallwood Algorithm:  Ahlin_SRS.pdf
Kelly and Richman, Principles and Techniques of Shock Data Analysis: SVM-5
Tustin and Hieber, Understanding and Measuring the Shock Response Spectrum: Tustin_SRS.pdf
Understanding the Use and Applications of the Shock Response Spectrum Method: SRS_method_DP.pdf

Methods for Converting a Power Spectral Density to a Shock Response Spectrum: psd_srs.pdf
Tuma & Koci, Calculation of the Shock Reponse Spectrum: TumaSRS_dm09.pdf
SRS Algorithm Limitations for a Rectangular Base Input:  SRS_rectangular_limit.pdf
A Digital Recursive Filtering Method for Calculating the Base Input for a Measured Response Acceleration:  DRFR_base_accel.pdf

Matlab script:  decon_arbit.m

A Digital Recursive Filtering Method for Calculating the Applied Force for a Measured Response Acceleration:  DRFR_applied_force.pdf

Matlab script:  decon_arbit_force.m

Amplitude Metrics

The Pseudo Velocity Shock Response Spectrum: pseudo_velox.pdf
Relative Displacement & Absolute Acceleration: srs_relative_displacement.pdf
Tripartite Shock Response Spectra Plots: tripartite.pdf
Matlab script: srs_tripartite.zip

dB/octave Calculations for Log-Log Plots:  dB_octave.pdf

SRS Test Specifications

Equivalence Methods for Shock Testing: equivalence_methods_shock.pdf 
T. Baca, Alternative Shock Characterization for Consistent Shock Test Specification: alternative_shock.pdf
Commercial Testing using the Shock Response Spectrum:  srs_comm.pdf 
Corresponding Synthesized Time History: synthesis.txt
An Alternative Method of Specifying Shock Test Criteria: NASA_TM_08_215253.pdf
R.C. Ferebee's Presentation:  Ferebee_shock.pdf

Synthesis & Waveform Reconstruction

Shock Response Spectrum Synthesis via Wavelets: srs_syn.pdf
Waveform Reconstruction using Wavelets: wavelet_reconstruction.pdf

Waveform Synthesis of the Pegasus Drop Transient for Shaker Table Shock Testing: Pegasus_Drop_Synthesis.pdf
Corresponding Time History Files: Drop_Syn.zip
Shock Response Spectrum Synthesis via Damped Sinusoids: srs_syn_dsine.pdf

Seismic Synthesis for Shaker Testing and Modal Transient FEA

Shaker Table Seismic Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy a Shock Response Spectrum
quake_syn.pdf
Matlab Scripts:
waveform_reconstruct.m
wavelet_scale_SRS_add.m
werror2.m
wqsrs.m
progressbar.m
th_from_wavelet_table.m
Wavelet Tables:
el_NS_wavelet_table.out
wavelet_40.txt
Time History:
accel_40.txt

Classical Shock Tutorials, Base Excitation & Initial Conditions,
SDOF Systems

Integrating the Acceleration Half-Sine Pulse: halfsine.pdf
Half-Sine Pulse Synthesis Via a Wavelet Series for Shaker Table Shock Tests: half_sine_synth.pdf
Matlab scripts: half_sine_synth.m & wgen_hs.m
Response of a Single-degree-of-freedom System Subjected to a Unit Step Displacement: unit_step.pdf 

Response of a Single-degree-of-freedom System Subjected to a Classical Pulse Base Excitation: sbase.pdf

Response of a Single-degree-of-freedom System Subjected to a Versed Sine Pulse Base Excitation: sbase_versed_sine.pdf

Response of a Single-degree-of-freedom System Subjected to a Terminal Sawtooth Base Excitation: terminal_sawtooth.pdf

The Response of a Single-degree-of-freedom System Subjected to a Wavelet Pulse Base Excitation: sbase_wavelet.pdf
Dynamic Load Factors for Classical Pulses, Charts: DLF_classical.pdf
The Fourier Transform of a Half-Sine Pulse: hs_fourier.pdf
Transportation Shock Due to Speed Bumps and Road Obstacles: bump.pdf

Partial Fractions in Shock and Vibration Analysis: partial.pdf
See also: Laplace Transforms in Shock & Vibration Analysis

Classical Shock Tutorials, Base Excitation & Initial Conditions, Two-DOF Systems

The Response of a Two-degree-of-freedom System Subjected to a Half-Sine Base Input Pulse: twodof_halfsine.pdf

The Response of a Two-degree-of-freedom System Subjected to a Wavelet Pulse Base Excitation:  twodof_wavelet.pdf
Classical Shock Tutorials, Applied Force, SDOF & Two-DOF Systems

Response of a Single-degree-of-freedom System Subjected to a Unit Step Force: force_unit_step.pdf

Matlab script:  unit_step_force.m
Response of a Single-degree-of-freedom System Subjected to an Impulse Force: force_impulse.pdf
Matlab script: impulse_force.m
Response of a Single-degree-of-freedom System Subjected to a Terminal Sawtooth Applied Force: terminal_sawtooth_force.pdf
Response of a Single-degree-of-freedom System Subject to a Half-Sine Applied Force: half_sine_force.pdf

Matlab script: half_sine_force.m

Response of a Two-degree-of-freedom System Subject to a Half-Sine Applied Force: two_dof_half_sine.pdf

Matlab script:
Matlab script:  twodof_half_sine_force.m

See also: Laplace Transforms in Shock & Vibration Analysis

Multi-Degree-of-Freedom Shock & FEA Shock

Shock Response of Multi-degree-of-freedom Systems:  mdof_srs.pdf
Methods for Combing Modes: combining_modes_SRS.pdf
Shock Response Spectrum Analysis via the Finite Element Method: FEA_shock.pdf
Nastran File: srs_plate_frf_4k.nas
Additional Files: FEA_Shock_files.zip
Shock Response Spectrum Synthesis via Damped Sinusoids: srs_syn_dsine.pdf

Impact & Drop Shock & Product Shock Fragility

See Impact Shock Page

Papers By David O. Smallwood
Sandia National Laboratories

Time History Synthesis for Shock Testing on Shakers: th_syn.pdf
An Improved Recursive Formula for Calculating Shock Response Spectra: DS_SRS1.pdf

The Shock Response Spectrum at Low Frequencies: low_srs.pdf
A Family of Transients Suitable for Reproduction on a Shaker Based on the cos^m(x) Window: cosine_transients.pdf

Pyrotechnic Shock, NASA & Military Documents

MIL-STD-810F, Method 517 Pyroshock: MIL810F_pyroshock.pdf
MIL-STD-810G, Method 517.1: MIL810G_pyroshock.pdf 
The Proposed NASA Pyroshock Test Criteria Standard: NASA_pyro2.pdf
NASA Pyrotechnic Shock Design Guidelines Manual: NasaPyro.zip
By Kacena, McGrath, and Rader.
NASA Pyroshock Test Criteria, by D. Kern: NASA-HDBK-7003
Pyroshock Data Acquistion and Analysis for U/RGM-109D Payload Cover Ejection Tests, NWC TP 6927, By Allan Piersol: Pyro_Data_AQ.pdf
NASA SP-8051 Solid Rocket Motor Igniters: sp8051.pdf

Pyrotechnic Shock Attenuation, Material & Joints

NASA Pyrotechnic Shock Design Guidelines Manual: NasaPyro.zip
By Kacena, McGrath, and Rader.

Martin Marrietta, Joint & Distance Attenuation: mm_shock.pdf
Attenuation of Longitudinal Shock Waves in a Rod: longitudinal_shock_att.pdf
Matlab Script: beam_long_initial_disp.m
Attenuation of Bending Shock Waves in a Beam: beam_shock_att.pdf
Matlab Script: beam_bending_initial_disp.m

Pyrotechnic Shock Simulation in the Test Lab

High G Pyrotechnic Shock Simulation Using Metal-to-Metal Impact: Bai.pdf
By Monty Bai and Wesley Thatcher
The Controlled Response of Resonating Fixtures Used to Simulate Pyroshock Enviroments, by Neil Davie: resonating_fixture.pdf
Summary of Testing Techniques, by Dan Powers: Powers_test.pdf
Multi-Degree-of-Freedom Pyrotechnic Shock Simulation, Slide Presentation, by Smith and Hollowell: mdof_sim.pdf
Comparison of Response from Different Resonant Plate Simulation Techniques: Morse_test.pdf
High Frequency Mechanical Pyroshock Simulation for Payload Systems, by Bateman, et al: payload_SRS.pdf
Pyrotechnic Shock Testing: Pyrotechnic Shock Testing: Real Test Lab Experiences at EBA&D, by Keon (slide presentation): EnsignBickford.pdf
Initial Velocity Excitation of the Longitudinal Modes in a Beam for Pyrotechnic Shock Simulation: iv_rod.pdf
Kolaini & Fernandez, JPL Tunable Beam Pyroshock Simulation System:  JPL_tunable_beam.pdf
J. Tiulaer, B. Allen, J. Maly, An Alternative to Pyrotechnic Testing for Shock Identification: CSA2007_pyrotechnic.pdf
Matlab script: beamvs.m

Pyrotechnic Shock Aliasing

The Need for Analog Anti-aliasing Filters in the Pyrotechnic Shock Testing of Avionics Components: AA_Filter_Pyro.pdf
Potential Aliasing in Pyrotechnic Shock Data: Numerical Experiments: aliasing_numerical_experiments.pdf
NASA Letter:  NTS_Pyroshock_NASA_KSC_Letter.pdf

Pyrotechnic Shock, Source Levels

Motor Ignition & Stage Separation Source Shock Library: source_shock.pdf
Release Nut Pyrotechnic Shock Energy Scaling: release_nut_energy_scaling.pdf
V-Band Source Shock Scaling: Vband_Scaling.pdf

Shock, Stress

Gaberson and Chalmers, Modal Velocity as a Criterion of Shock Severity, Shock and Vibration Bulletin, Naval Research Lab, December 1969: modal_velocity.pdf

Shock and Vibration Stress as a Function of Velocity: sv_velocity.pdf

Pyrotechnic Shock, Other

Measuring and Analysis of Pyrotechnic Shock: pyroshoc.pdf
Submitted by John Eriksson and Mattias Hansson, Chalmers University of Technology, Sweden. Vibrationdata student paper contest, Spring 2000.

V. Bateman, The Validation of Pyroshock data:  24_Besta_Bateman_website.pdf
Pyrotechnic Shock Flight Failures By C.J. Moening (three versions):
Moening.pdf
 , Moening.doc
Pyrotechnic_Shock_Failures_Moening.pdf
Mechanical Shock from Frangible Joints, by V.R. Paul: frangible_joints.pdf
Pyrotechnic Shock Structural Response, by R.G. Merritt: Merritt.pdf
Structural Response to an Applied Point Force in Terms of Mechanical Impedance: shock_impedance.pdf

Saturation Removal

A Mean Filter Method for Removing Saturation from Pyrotechnic Shock Pulses: mean_filter_saturation_removal.pdf
An Improved Mean Filter Method for Removing Saturation from Pyrotechnic Shock Pulses: improved_sat_remove.pdf
Data Sample: pyro_sat.txt
Software: sat_remove5.exe

V-band Pyroshock

V-Band Separation Shock Characteristics, by K.Y. Chang: V_Band.pdf
V-Band Source Shock Scaling: Vband_Scaling.pdf
V-Band Structural Analysis: Vband_Structural Analysis.pdf

Dynamic Design Analysis Method (DDAM)

Moved to:  Shipboard Shock & Vibration

Seismic Shock

Moved to: Seismology and Earthquake Engineering

Sine, Random and Shock Equivalence 

A Method for Using an Equivalent Shock Specification to Cover a Pure Sine Vibration Requirement shock_sine.pdf
Matlab script: shock_sine.m
The Equivalent Sine of an SRS: equivalent_sine_SRS.pdf
Shock and Random Vibration Equivalence: shock_vib_eq.pdf

Avionics & Circuit Board Response to Shock

Designing Electronics for Pyrotechnic Shock: Luhrs.pdf
By Henry Luhrs
Shock & Vibration Fatigue Criteria for Electrical Components: ec_fat.pdf
Shock Analysis of Avionics Mounting Bolts: shock_bolts.pdf
Crystal Oscillator Mounting for Shock and Vibration: crystal_mount.pdf 

Low-Cycle Shock Fatigue of Electronic Components:  low_cycle_fatigue.pdf

Qualification Shock Testing for Reusable Avionics Components:  shock_reuse.pdf
Other Vibrationdata Pages: HomeTutorials | Search

 

 SRS Software

 Matlab Codes
SRS Matlab Code
srs.m
SRS via convolution
srs_conv.m
Tripartite Shock Response Spectra Plots:
srs_tripartite.m

Supporting functions: srs_coefficients.m
enter_time_history.m

Mean filter method for removing saturation with optimization.

mean_filter_saturation.m

mr_SRS.m

Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input:  
arbit.m

Supporting functions:
srs_coefficients.m

enter_time_history.m
Waveform reconstruction via wavelets.
waveform_reconstruct.m
wgen.m
Scale a wavelet table to match an SRS specification.
wavelet_scale_SRS.m
wqsrs.m
werror.m
Additional Matlab shock programs are given at: Matlab

 

Base Excitation Shock Software
Description
Executable
Source Code
Shock response spectrum of an arbitrary acceleration time history. The user must supply the input time history file. The input file would typically be the userís measured accelerometer data.
DOS version: qsrs.exe
Windows version: srs.exe
Matlab version:
srs.m
Supporting functions:

srs_coefficients.m

enter_time_history.m


fix_size.m
find_max.m


C++ Linux version:
Linux_qsrs

Type:  chmod +x Linux_qsrs
Use :  ./Linux_qsrs

Java version:
Java_SRS.jar

To run the java file from the terminal type: 
java -jar Java_SRS.jar

 qsrs.cpp
 
 
Java_SRS.zip
Calculate the maximax SRS from a positive and negative SRS.
maxsrs.exe
maxsrs.cpp
Response of a single-degree-of-freedom system to base excitation, where the excitation is a classical pulse. Answers the question,  "What is the shock response spectrum of a  half-sine pulse?"
  pulse.exe

 _

Response of a single-degree-of-freedom system to a half-sine base input acceleration pulse.
 ahsine.exe
 ahsine.cpp
Response of a single-degree-of-freedom system to a terminal sawtooth input acceleration pulse.
terminal_sawtooth.exe
terminal_sawtooth.cpp
Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input via a digital recursive filtering relationship
 arbit.exe
  arbit.cpp
Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input via a digital recursive filtering relationship with rainflow cycle counting arbit_rainflow.exe arbit_rainflow.cpp
 Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input via a convolution integral
arbit_convolution.exe arbit_convolution.cpp
Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input via the Newmark-beta method. arbit_newmark.exe arbit_newmark.cpp
Time history response of a single-degree-of-freedom system to an arbitrary base input via the Runge-Kutta Fourth Order method. arbit_rk4.exe arbit_rk4.cpp
Calculate the relative displacement from an acceleration SRS
SRS_rel_disp.exe
SRS_rel_disp.cpp
 Eigenvalues and eigenvectors of a two-degree-of-freedom system.
 twodof.exe
  twodof.cpp
Time history response of a two-degree-of-freedom system to an arbitrary acceleration base input.
two_dof_arbit.exe
two_dof_arbit.cpp
Time history response of a two-degree-of-freedom system to a half-sine acceleration base input.
twodof_halfsine.exe
twodof_halfsine.cpp
Identify the natural frequency, damping and excitation parameters for a system subjected to a half-sine base acceleration pulse.
find_halfsine.exe
find_halfsine.cpp
Identify the natural frequency, damping and excitation parameters for a system subjected to a wavelet base acceleration pulse.
find_wavelet_response.exe
find_wavelet_response.cpp


Applied Force Shock Software

Description
Executable
Source Code
Response of a single-degree-of-freedom system to a terminal sawtooth applied pulse.
terminal_sawtooth_force.exe
terminal_sawtooth_force.cpp
Time history response of a single-degree-of-freedom system to an arbitrary applied force via a digital recursive filtering relationship.
arbit_f.exe
arbit_f.cpp
Time history response of a single-degree-of-freedom system to an arbitrary applied force via the Newmark method. arbit_newmark_force.exe arbit_newmark_force.cpp
Time history response of a single-degree-of-freedom system to an arbitrary applied force via the Runge-Kutta fourth order method. arbit_rk4_force.exe arbit_rk4_force.cpp
Response of a single-degree-of-freedom system to a half-sine force input pulse.
fhsine.exe
fhsine.cpp
Shock response spectrum for an applied force.
fsrs.exe
fsrs.cpp

SRS Synthesis
Description
Executable
Source Code
Synthesis of a time history to satisfy a shock response spectrum specification. The time history consists of damped sinusoids. This program is intended mainly for modal transient analysis.
(formerly known as srs_syn.cpp)
damped_sine_syn.exe
srs_syn_dsine.pdf
damped_sine_syn.cpp
Matlab version
damped_sine_syn.m
Supporting functions:

DSS_sintime.m
DSS_th_syn.m
DSS_wgen.m
DSS_srs.m
DSS_scale_th.m
DSS_srs_error.m
DSS_waveform_reconstruction.m

plot_avd_srs.m
integrate_function.m

srs_coefficients.m
progressbar.m

fix_size.m

add_pre_shock.m


Synthesis of a time history to satisfy a shock response spectrum specification using wavelets. This program is particularly useful for shaker shock testing.
(formerly known as jsynth.cpp)
wavelet_synth.exe

srs_syn.pdf 

jsynth_user_manual.pdf
wavelet_synth.cpp

Matlab version

wavelet_synth.m

Supporting functions

ws_th_from_wavelet_table.m
ws_rankfunctions.m
ws_scale.m
ws_srs_error.m
ws_gen_time.m
ws_max_param.m
ws_synth3.m
ws_synth1.m
ws_srs.m

srs_coefficients.m
plot_avd_time_histories.m wavelet_synth_srs_plot.m

Alternate version

wavelet_synth_alt.m
ws_rankfunctions_alt.m

Generate time history from wavelet table.

th_wavelet.exe

th_wavelet.cpp

Synthesis of a time history to satisfy a shock response spectrum specification using wavelets including a specified ZPA.
jsynth_ZPA.exe
jsynth_ZPA.cpp
Scale a wavelet table to match an SRS specification.
wavelet_scale_SRS.exe
wavelet_scale_SRS.cpp
Synthesis of a time history to satisfy a shock response s spectrum using wavelets with random time delays. This program could be used either for shaker shock or for a modal transient analysis.
seismic_synth.exe
seismic_synth.cpp

 

Waveform Reconstruction 
Description
Executable
Source Code
Synthesize a time history using wavelets to represent a measured time history. This program is useful for shaker shock.
wavelet_reconstruct.exe
wavelet_reconstruct.cpp
Wavelet synthesis with a preference for logarithmically spaced frequencies. wavelet_reconstruct_alt.exe wavelet_reconstruct_alt.cpp
Synthesize a time history using wavelets to represent a pyrotechnic time history. This program is useful for estimating the velocity and displacement of a pyrotechnic pulse.
pyro_reconstruct.exe
pyro_reconstruct.cpp
Addition of shock pulses.
composite_shock.exe
composite_shock.exe

Saturation Removal Software
Description
Executable
Source Code
Mean filter method for saturation removal, manual selection of window size and number of passes.
mf_saturation.exe
mf_saturation.cpp
Mean filter method for saturation removal, manual s election of upper limits for window size and number of passes, automatic with optimization.
mean_filter_saturation.exe
mean_filter_saturation.cpp
Median filter method for saturation removal, manual selection of upper limits for window size and number of passes, automatic with optimization.
median_filter_saturation.exe
median_filter_saturation.cpp
Piecewise linear trend removal to remove spurious baseline shifts and saturation effects. Requires engineering judgment.
piecewise_linear_remove.exe
piecewise_linear_remove.cpp
Remove saturation indirectly by specifying an initial SRS ramp. The program then uses a piecewise linear trend removal approach to match the SRS ramp as closely as possible.
sat_remove5.exe
sat_remove5.cpp
Remove saturation by specifying an SRS slope and ending coordinate.
slope_meet.exe
slope_meet.cpp
Remove saturation by indirect filtering.
indirect_filter.exe
indirect_filter.cpp
Miscellaneous Shock Software
Description
Executable
Source Code
Multifunction Shock Program

1. Response of a single-degree-of-freedom system to a simple drop shock. Useful for evaluating accidental drops.
2. Drop table velocity and rebound spring displacement for a half-sine shock test.
Shock.exe

  _

 Energy Spectral Density
 espec.exe
 espec.cpp
 Pyrotechnic shock attenuation from joints, distance, and isolators.
pyro_atten.exe
 pyro_atten.cpp
NASA Pyrotechnic Shock Design Guidelines Manual, attenuation through a cylindrical shell.

cylindrical_atten.exe

cylindrical_atten.cpp
Principal strains from dynamic strain data using Mohr's circle for a rosette.
mohr_rosette.exe
mohr_rosette.cpp
Interpolate an SRS to octave format.
interp_SRS.exe
interp_SRS.cpp
Cumulative RMS of a time history. Used as an alternate tool for shock severity evaluation.
TRMS.exe
TRMS.cpp
Histogram, probability density function, and peak distribution of a time history.
histogram.exe
histogram.cpp
Calculate relative displacement from absolute acceleration and vice versa.
DOS Version:
relative_displacement.exe
Windows Version:
SRS_relative_displacement.exe
relative_displacement.cpp
Generate shock pulses.
generate_pulse.exe

-

Generate wavelet.
wavelet_gen.exe

-

Determine the percentage of points from a measured SRS that are > nominal specification.
srs_test_spec.exe
srs_test_spec.cpp
Unit conversion program.
units.exe
DLL files:
mfc100u.dll
msvcr100.dll

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