Shock response spectrum

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A Shock Response Spectrum (SRS) is a misleadingly named, graphical concept used in comparing the effects different shocks are likely to have on a structure or piece of equipment.

An SRS is generated from a shock waveform using the following process:

Pick a damping ratio for your SRS to be based on
Assume a Single Degree of Freedom System (SDOF), with a damped natural frequency of xHz
Calculate (by time base simulation or something more subtle) the maximum instantaneous absolute acceleration experienced by the mass of your SDOFs at any time during (or after) exposure to the shock in question. Plot this in g's (g's are standard, but pick any unit of acceleration you want) against the frequency (x) of the system.
Repeat steps 2 and 3 for other values of X, say logarithmically up to 1000x.

The resulting plot called a Shock Response Spectrum. The name is misleading because simply plotting a list of "something versus frequency" does not make it a spectral plot (no more than a chart showing your probability of bumping your head on the doorframe versus your height means there's a steady stream of heads being bumped).

An SRS is useful if you want to compare two shocks and can convince yourself that the equipment or structure in question can be seen as a family of largely independent linear systems. The idea is that you're plotting what each of those little subsystems would see as a maximum stress.

The SRS also can be regarded in terms of "equivalent steady-state (sinusoidal) vibration." Comparing the SRS divided by the amplification factor (Q) provides a measure for an equivalent steady-state or harmonic (sinusoidal) input resulting in the same maximum vibration level. This allows a comparison of transient or generally non-stationary accelerations to steady-state or harmonic (sinusoidal) vibrations, which might be especially interesting when qualifying or testing systems.

Consider, for example, a computer chassis containing three cards with fundamental natural frequencies of aHz, bHz, and cHz, and a screen with a predicted frequency of dHz. The system is tested to a certain shock waveform (based on recorded data from the customer's application) in the lab. A new customer comes along, and you want to be able to determine whether or not the computer is likely to survive the shocks measured in their application. You could calculate the SRS of each shock, and check that in the neighbourhood of the card/screen's maximum sensitivities the new shock is lower than the old one, and that everywhere else it's not too much higher. If so, you've got a good indication that it's likely to survive.

Note that any shock waveform can be presented as an SRS, but the relationship is not unique; many different shock waveforms can produce the same SRS (which one can take advantage of through a process called "Shock Synthesis"). The SRS does not contain all the information in the shock waveform from which it was created.

Note that different damping ratios produce different SRSs for the same shock waveform. Zero damping is undefined, because the response never stops, so you can't calculate a maximum. Very high damping produces a very boring SRS (horizontal line).

Note that an SRS is useless for fatigue-type damage scenarios, as the information of how many times a peak stress is reached is lost in the transform.

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