There is a need in certain structural dynamics finite element analysis problems to perform a response analysis in the time domain. This would be the case, for example, if the stiffness was non-linear. Loss-of-clearance or contact between two adjacent vibrating parts is another analysis example.

Consider the case of base excitation in the form of a PSD. A time history can be readily synthesized to satisfy the PSD. The corresponding number of time history samples may overwhelm the finite element program’s allowable array sizes or cause excessive processing time and memory usage, however.

Certain military and aerospace PSD specifications have an upper frequency of 2000 Hz. A synthesized time history should thus have a sample rate of at least 20 KHz, which is ten times the highest PSD frequency. The total number of time history points would be 1.2 million if the specified duration was 60 seconds.

Now consider that the peak response must be calculated and that fatigue is unimportant. This would be the case for evaluating the resulting response with respect to yielding, ultimate stress limit, or relative displacement.

A shorter duration time history can be synthesized to satisfy this need as presented in this paper: Abbreviated_FEA_Transient.pdf

The abbreviated time history is derived using response spectra. Its response spectrum must envelop that of the full-duration PSD as determined from Rayleigh distribution of the PSD response.

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Matlab Scripts for this Method:

VRS.zip

srs_sine_syn.zip

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See also:

SDOF Response to an acceleration PSD Base Input

Peak Response for Random Vibration

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– Tom Irvine

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