Shock Response Spectrum (SRS)

Category: Structural Analysis | Integrated 2026-04-06
CAE visualization for shock response spectrum theory - technical simulation diagram
Shock Response Spectrum (SRS)

Shock Response Spectrum (SRS): Theoretical Foundations

What is SRS?

๐Ÿง‘โ€๐ŸŽ“

Professor, is SRS (Shock Response Spectrum) the same concept as the seismic response spectrum?


๐ŸŽ“

The concept is the same, but the input is different. The seismic response spectrum is the maximum response to "seismic waveforms", while SRS is the maximum response to shock waveforms (half-sine wave, pyroshock, etc.).


$$ SRS(f_n) = \max_t |x(t; f_n, \zeta)| $$

๐Ÿง‘โ€๐ŸŽ“

Shock test standards are often specified using SRS, right?


๐ŸŽ“

MIL-STD-810 Shock tests and NASA-STD-7003 pyroshock environments are specified using SRS. It's used to verify if the test input waveform satisfies the SRS specification.


Types of SRS

๐ŸŽ“
  • Primary SRS โ€” Maximum response during the shock input
  • Residual SRS โ€” Maximum response after the shock input (during free vibration)
  • Maximax SRS โ€” Maximum value of Primary + Residual

  • SRS Calculation in FEM

    ๐ŸŽ“

    1. Perform time history analysis (modal method or direct method or explicit method) to calculate the response

    2. Generate SRS in post-processing โ€” Plot the maximum response of a single-degree-of-freedom system for each natural frequency


    Summary

    ๐ŸŽ“

    Key Points:


    • SRS = Maximum response for each natural frequency to shock โ€” The shock version of the seismic spectrum
    • Specified in MIL-STD-810, NASA-STD-7003 โ€” Standards for shock testing
    • Primary / Residual / Maximax โ€” During shock vs. after shock
    • FEM time history โ†’ SRS generation in post-processing โ€” Nastran PARAM,SRS

    Coffee Break Yomoyama Talk

    SRS originated from predicting shock damage in nuclear tests

    The Shock Response Spectrum (SRS) was developed by NASA/the military in the 1960s for evaluating the shock resistance of equipment/structures during nuclear tests. The formal mathematical formulation was published by C.V. Nagel and D.S. Bernstein in 1969. It was later incorporated into IEC 60068-2-27 (shock testing) and MIL-STD-810G (transportation vibration/shock), and is now a design standard for space equipment and military electronics.

    Computational Methods for Shock Response Spectrum (SRS)

    SRS Calculation

    ๐ŸŽ“

    Numerical calculation of SRS is "simultaneous time integration of many single-degree-of-freedom systems":


    For each natural frequency $f_n$ (10 Hz to 10 kHz, e.g., 1/3 octave intervals):

    1. Time-integrate the equation of motion for a single-degree-of-freedom system (Newmark method, etc.)

    2. Record the maximum response (acceleration or displacement or pseudo-velocity)

    3. Plot $f_n$ vs. maximum response โ†’ SRS


    Solver SRS Output

    ๐ŸŽ“
    • Nastran: PARAM,SRS + SOL 112
    • Abaqus: Python script for post-processing
    • Ansys: POST26 + SRS calculation
    • MATLAB/Python: Implement custom SRS function (most flexible)

    • Summary

      ๐ŸŽ“
      • Time integration of many single-degree-of-freedom systems โ€” Maximum response for each $f_n$
      • Calculated in post-processing โ€” From FEM time history results
      • MATLAB/Python SRS calculation is the most flexible

      • Coffee Break Yomoyama Talk

        Minimum damping for SRS calculation is 2%, an industry standard

        For SRS calculation, a damping ratio ฮถ = 5% is the MIL-STD-810 standard, but for ultra-sensitive equipment (gyros, accelerometers), actual damping is often below 2%, so calculating SRS with ฮถ = 2% is also required per NASA-STD-7003A (2011). Changing the damping ratio from 5% to 2% can increase SRS peak values by up to 1.5 times, significantly impacting design margin evaluation.

        Shock Response Spectrum (SRS) in Practice

        SRS in Practice

        ๐ŸŽ“

        Essential for pyroshock environment evaluation of space equipment and shock testing of military electronics.


        Practical Checklist

        ๐ŸŽ“
        • [ ] Does the SRS damping ratio (typically $Q = 10$, $\zeta = 5\%$) match the standard?
        • [ ] Does the SRS frequency range cover the standard?
        • [ ] Is the SRS within the standard's envelope?
        • [ ] Does the FEM time history have sufficient frequency resolution ($\Delta t < 1/(10 f_{max})$)?
        • [ ] Are enough frequency points used for SRS calculation (1/6 octave or finer)?

        • Coffee Break Yomoyama Talk

          Satellite separation shock reaches 1000โ€“10000G

          During the instant of satellite separation from a rocket via pyrobolt (explosive device) detonation, the structure experiences instantaneous peak accelerations of 1000โ€“10000G. JAXA's H-IIA-mounted satellites specify separation shock SRS (ฮถ=5%, 10โ€“10000Hz) in their specifications, with pass/fail determined by pre-launch shock tests. For ASTROS-H (launched 2016), detailed SRS prediction using ESI Crash/PAM-SHOCK was performed for separation shock analysis.

          Shock Response Spectrum (SRS): Software & Solver Comparison

          SRS Tools

          ๐ŸŽ“
          • Nastran SOL 112 + PARAM,SRS โ€” SRS output from FEM
          • Vibration Research โ€” Vibration test control + SRS calculation
          • MATLAB Signal Processing Toolbox โ€” SRS function
          • Python (scipy) โ€” Custom SRS calculation. Most flexible

          • Selection Guide

            ๐ŸŽ“
            • SRS evaluation from FEM โ†’ Nastran SOL 112
            • SRS processing of test data โ†’ Vibration Research or MATLAB
            • Custom SRS calculation โ†’ Python (scipy single-degree-of-freedom integration)

            • Coffee Break Yomoyama Talk

              Dewesoft and Data Physics Compete for SRS Analysis Market Share

              The SRS analysis software market is divided between Dewesoft (Slovenia, founded 2000) and Data Physics (USA, founded 1984). Dewesoft's DS-NET PRO integrates data acquisition, SRS calculation, and MIL-STD-810 compliance reporting, with industry-leading processing speed (1 million points/sec). For CAE integration, a plugin connecting Ansys Motion's SRS input function directly with Dewesoft measurement values has been available since 2022, enabling rapid correlation verification between experiment and analysis.

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