Non-Gaussian Acoustic Pressure Amplitudes in High-Intensity Sound Fields

“Shock Diamonds” in the afterburner of a NASA SR-71B Jet

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Sound pressure levels are limited by the physical characteristics of the surrounding medium.

The ambient air pressure at sea level is “one atmosphere,” or approximately 14.7 psi on the absolute scale.

The absolute pressure in an ideal vacuum is zero psi.

The “laws of practical physics” do not allow a sound wave to have a minimum pressure level of zero psi absolute, however.  Various thermodynamic and molecular chemistry effects intervene well before this limit would be reached.

The philosopher Baruch Spinoza (1632-1677) wrote “Nature abhors a vacuum.”

This observation is particularly true in acoustic fields, where distortion begins at levels as low as 159 dB, or 0.25 psi RMS, as nonlinear restraining mechanisms begin to counteract the forming void.

The resulting sound pressure time history become skewed with high positive pressure peaks.

Examples from aerospace vehicles are given in: nongaussian_acoustics

Sample time history from the above paper:

See also: Vibrationdata Rocket Page

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Numerical studies of this effect can be simulated by generating random time histories with user-defined skewness and kurtosis parameters.  A Matlab script for this simulation is:  white_kurtosis_skewed.m with supporting function progressbar.m

The resutling time history can then be applied to a dynamic model as a forcing function.

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A function for generating a random time history corresponding to the Student t distribution is given in: Vibrationdata Signal Analysis Package

This allows for kurtosis values > 3 with zero skewness.

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– Tom Irvine

One thought on “Non-Gaussian Acoustic Pressure Amplitudes in High-Intensity Sound Fields

  1. I recommend using the Hermite polynomial transformation to generate a random time series with a specified PSD, skewness and kurtosis. This method may distort the PSD somewhat in extreme cases. I never had this happen in my experience though.

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