Shock Response Spectrum

A Shock Response Spectrum (SRS) is a graphical presentation of a transient acceleration pulse’s potential to damage a structure. It plots the peak acceleration responses of a bank of single degree-of-freedom (SDOF) spring, mass damper systems all experiencing the same base-excitation as if on a rigid massless base. Each SDOF system has a different natural frequency; they all have the same viscous damping factor. A spectrum results from plotting the peak accelerations (vertically) against the natural frequencies (horizontally). An SRS is generated from a shock waveform using the following process:

  • Specify a damping ratio for the SRS (5% is most common)
  • Use a digital filter to model an SDOF of frequency, fn and damping ξ.
  • Apply the transient as an input and calculate the response acceleration waveform.
  • Retain the peak positive and negative responses occurring during the pulse’s duration and afterward.
  • Select one of these extreme values and plot it as the spectrum amplitude at fn.
  • Repeat these steps for each (logarithmically spaced) fn desired.

Illustration of a multi-degree of freedom system model used to compute SRS.