A boundary element based method for accurate prediction of the surface pressure cross-spectral density matrix

Abstract

Accurate prediction of the surface pressure cross-spectral density matrix is necessary to predict the dynamic response of a structure loaded by a diffuse acoustic field. The cross-spectral density matrix describes the frequency dependence of the correlation between the surface pressure at all pairs of points on the structure. Most often the cross-spectral density matrix is obtained from either a uniform distribution of incident plane waves or direct application of the diffuse field spatial cross-correlation function. While the method of plane waves is relatively more accurate, especially at low frequencies, the necessary distribution of incidence angles and ensemble size can be problematic. This talk shall present a boundary element based methodology for determining the surface pressure cross-spectral density for any structure and frequency, including the effects of scattering and shielding. The method involves a power spectral density formulation of the boundary element method and takes advantage of the underlying foundations in potential theory. The method can be generalized beyond diffuse fields and can be applied to structures having a known surface impedance.

A comparison between the high-frequency Boundary Element Method and Surface-Based Geometrical Acoustics

“…Both methods solve for pressure distributions satisfying the wave equation, so their results can simply be summed arithmetically. SB-GA differs because it is based on energy, so transfer will likely involve stochastic energy statements [19].…”

“…7. This leads to cross-terms involving spatial cross-correlations [19], meaning 𝑎 𝑞 is most likely related to 𝑏 𝑛 through a Wigner transform [27]. This is, however, an open research question.…”