Sound propagation over the ground with a random spatially-varying surface admittance

The Journal of the Acoustical Society of America
Didier Dragna, Philippe Blanc-Benon

Abstract

Sound propagation over the ground with a random spatially-varying surface admittance is investigated. Starting from the Green's theorem, a Dyson equation is derived for the coherent acoustic pressure. Under the Bourret approximation, an explicit expression is deduced and an effective admittance that depends on the correlation function of the admittance fluctuations is exhibited. An asymptotic expression at long range is then obtained. Influence of the randomness on the amplitude of the reflection coefficient and on the wavenumbers of the surface wave component is analyzed. Afterwards, numerical simulations of the linearized Euler equations are carried out and the coherent pressure obtained by an ensemble-averaging over 200 realizations of the admittance is found to be in good agreement with the analytical solution. In the considered examples of grounds, the mean intensity is shown to be similar to the intensity in the non-random case, except near interferences that are smoothened out due to randomness. It is however exemplified that the intensity fluctuations can be large, especially near destructive interferences.

References

Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Arnaud DerodeArnaud Tourin
Jun 7, 2007·The Journal of the Acoustical Society of America·D Keith WilsonPeter P Sullivan
Oct 7, 2011·The Journal of the Acoustical Society of America·Vladimir E OstashevSergey N Vecherin
Apr 6, 2013·The Journal of the Acoustical Society of America·Loïc EhrhardtPhilippe Blanc-Benon
Jun 8, 2013·The Journal of the Acoustical Society of America·Didier DragnaFranck Poisson
Mar 13, 2014·The Journal of the Acoustical Society of America·Didier DragnaFranck Poisson
Nov 2, 2015·The Journal of the Acoustical Society of America·Didier DragnaPhilippe Blanc-Benon

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