Welcome to Vibrationdata Pyrotechnic Shock &
Shock Response Spectrum Page

 Figure 1.  Launch Vehicle Stage Separation Test

The source device is linear shape 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.

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

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.m

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

SRS Test Specifications

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

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

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

Response of a Single-degree-of-freedom System Subjected to a Terminal Sawtooth Applied Force: terminal_sawtooth_force.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

Transportation Shock Due to Speed Bumps and Road Obstacles: bump.pdf

Partial Fractions in Shock and Vibration Analysis: partial.pdf

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 and Drop Shock

Simple Drop Shock: dshock.pdf

Horizontal Impact Shock: h_impact.pdf

Water Impact Shock: water_impact.pdf

Equivalent Bench Handling Shock Response Spectrum: bench_handling.pdf

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

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

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.

Pyrotechnic Shock Flight Failures: Moening.pdf  , Moening.doc
By C.J. Moening

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

O'Hara and Cunniff, Time History Analysis of Systems as an Alternative to DDAM-Type Analysis: DDAM1.pdf

NRL Report 7396 Shipboard Shock and Navy Devices for Its Simulation: NR_7396.pdf

NRL Memorandum Report 1396, Interim Design Values for Shock Design of Shipboard Equipment: NR_1396.pdf

MIL-S-901 Barge Test Video: barge_shock.mpg

See also Shipboard Shock & Vibration

Seismic Shock

Seismic Response Spectra: seis_rs.pdf

See also: Seismology and Earthquake Engineering

Sine 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

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 

Other Vibrationdata Pages: Home | Tutorials | Search

 SRS Software

 Matlab Codes

Additional Matlab shock programs are given at: Matlab

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 user’s measured accelerometer data.

DOS version:
qsrs.exe

Windows version:
srs.exe

 qsrs.cpp

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.

 arbit.exe

  arbit.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

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.

arbit_f.exe

arbit_f.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

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 script & functions:

damped_sine_syn.m

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

Synthesis of a time history to satisfy a shock response 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

Synthesis of a time history to satisfy a shock response spectrum specification using wavelets including a specified ZPA.

 jsynth_ZPA.exe

jsynth_ZPA.cpp

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

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

Scale a wavelet table to match an SRS specification.

wavelet_scale_SRS.exe

wavelet_scale_SRS.cpp

Addition of shock pulses.

composite_shock.exe

composite_shock.cpp

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

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.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