Enveloping Random Vibration PSD Functions

These Matlab scripts determine an optimum envelope for an acceleration power spectral density: envelope_plateau.zip

The optimum envelope is the that which yields the lowest GRMS and Velocity RMS values.

The acceleration is assumed to be the base excitation for an array of independent, parallel single-degree-of-freedom systems. The vibration response spectrum method is used to justify the envelope.  This provides a rational method for peak-clipping.

The damping ratio is fixed at 0.05, equivalent to Q=10. The natural frequency is an independent variable.

The user must input a power spectral density file.

The file must be ASCII text with two columns:

Freq(Hz) PSD(G^2/Hz)

The main script is envelope_plateau.m

The remaining functions are supporting functions.

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The above scripts generate an optimum PSD which has a series of ramps and plateaus.

Here are the original scripts which generate a more free-form PSD: envelope.zip

The main script is envelope.m

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envelope.zip also contains a script:  envelope_srs_psd.m.

This script can be used to derive a PSD to envelop an SRS.  The script uses the Rayleigh distribution to determine the n-sigma peak for each natural frequency based on the the product of the the natural frequency and duration.

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See also:

Optimized PSD Envelope for Nonstationary Vibration

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– Tom Irvine

2 thoughts on “Enveloping Random Vibration PSD Functions

  1. Dear Tom,
    The code seems interesting, however I think there is a file/function missing: “env_make_input_vrs.m”. Or at least, I could not make it work as Matlab is complaining about that file missing.
    Anyway, I will keep reading and analysing it to see if I can fix it.

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