Shock response spectrum

The most direct and intuitive way to generate an SRS from a shock waveform is the following procedure:[2]

1. Pick a damping ratio (or equivalently, a quality factor Q) for your SRS to be based on;
2. Pick a frequency f, and assume that there is a hypothetical Single Degree of Freedom (SDOF) system with a damped natural frequency of f ;
3. Calculate (by direct time-domain simulation) the maximum instantaneous absolute acceleration experienced by the mass element of your SDOF at any time during (or after) exposure to the shock in question. This acceleration is a;
4. Draw a dot at (f,a);
5. Repeat steps 2–4 for many other values of f, and connect all the dots together into a smooth curve.

The resulting plot of peak acceleration vs test system frequency is called a Shock Response Spectrum. It is often plotted with frequency in Hz, and with acceleration in units of g

Consider a computer chassis containing three cards with fundamental natural frequencies of f₁, f₂, and f₃. Lab tests have previously confirmed that this system survives a certain shock waveform—say, the shock from dropping the chassis from 2 feet above a hard floor. Now, the customer wants to know whether the system will survive a different shock waveform—say, from dropping the chassis from 4 feet above a carpeted floor. If the SRS of the new shock is lower than the SRS of the old shock at each of the three frequencies f₁, f₂, and f₃, then the chassis is likely to survive the new shock. (It is not, however, guaranteed.)

Any transient waveform can be presented as an SRS, but the relationship is not unique; many different transient waveforms can produce the same SRS (something one can take advantage of through a process called "Shock Synthesis"). Due to only tracking the peak instantaneous acceleration the SRS does not contain all the information in the transient waveform from which it was created.[3]

Different damping ratios produce different SRSs for the same shock waveform. Zero damping will produce a maximum response. Very high damping produces a very boring SRS: A horizontal line. The level of damping is demonstrated by the "quality factor", Q which can also be thought of transmissibility in sinusoidal vibration case. Relative damping of 5% results in a Q of 10. An SRS plot is incomplete if it doesn't specify the assumed Q value.[3]

An SRS is of little use for fatigue-type damage scenarios, as the transform removes information of how many times a peak acceleration (and inferred stress) is reached.[3]

The SDOF system model also can be used to characterize the severity of vibrations, with two criteria:

• the exceeding of characteristic instantaneous stress limits (yield stress, ultimate stress etc.). We then define the extreme response spectrum (ERS), similar to the shock response spectrum;
• the damage by fatigue following the application of a large number of cycles, thus taking into account the duration of the vibration (Fatigue damage spectrum (FDS)).

Like many other useful tools, the SRS is not applicable to significantly non-linear systems.

• Shock data logger
• Shock detector

• Harris, C., Piersol, A., Harris Shock and Vibration Handbook, Fifth Edition, McGraw-Hill, (2002), ISBN 0-07-137081-1 .
• Lalanne, C., Mechanical Vibration and Shock Analysis. Volume 2: Mechanical Shock, Second Edition, Wiley, 2009.
• MIL-STD-810G, Environmental Test Methods and Engineering Guidelines, 2000, sect 516.6

FreeSRS, http://freesrs.sourceforge.net/, is a toolbox in the public domain to calculate SRS.