Shock Response Spectrum

 The most widely used algorithm for the Shock Response Spectrum (SRS) calculation for base excitation is the ramp invariant digital recursive filtering relationship given in:

David O. Smallwood, An Improved Recursive Formula for Calculating Shock Response Spectra, Shock and Vibration Bulletin, No. 51, May 1981.  The link is:  DS_SRS1.pdf

Smallwood duly gave the resulting filtering coefficients in his paper, but he omitted the derivation details for brevity.

This omission is typical for papers published in journals and conference proceedings, given that derivations may require dozens of steps.

The SRS derivation requires impulse response functions, Laplace transforms and Z-transforms.

The following paper fills in the details:  ramp_invariant_base.pdf

Additional papers are given at: Vibrationdata SRS

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Here is a Matlab script for the SRS calculation of an arbitrary base input pulse: srs.m

Supporting functions:
srs_coefficients.m
enter_time_history.m

fix_size.m
find_max.m

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Here is a Matlab script for the time history response of a specific SDOF system to an arbitrary pulse: arbit.zip

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Here is a Matlab script for the SRS of a half-sine pulse & its supporting function:  halfsine.m  & time_calc.m

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A Fortran SRS program is given at:  QSRS.F

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See also:

SRS Educational Animation

Python SRS

Synthesize an Acceleration Time History to Satisfy a Shock Response Spectrum

SRS Tripartite

Pyrotechnic Shock Characterization Testing

Pyrotechnic Shock Joint Attenuation

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- Tom Irvine
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