An equivalent source technique for calculating the sound field inside an enclosure containing scattering objects

Abstract

The equivalent source method has previously been used to calculate the exterior sound field radiated or scattered from bodies in the free-field. In this paper the method is used to calculate the internal pressure field for an enclosure which can have arbitrary boundary conditions and may include internal objects which scatter the sound. Some of the equivalent source positions are chosen to be the same as the first order images of the source inside the enclosure, some are positioned within the scattering objects, and the remainder are positioned on a spherical surface some distance outside the enclosure. The normal velocity on the surfaces of the scattering objects and the enclosure walls is evaluated at a larger number of positions than there are equivalent sources. The sum of the squared difference between this velocity and that expected because of the admittance of the boundary, is minimized by adjusting the strengths of the equivalent sources. The convergence of the method is checked by evaluating the velocity at a larger number of monitoring positions. Example results are presented for the sound field and frequency response inside a damped rectangular enclosure, which compare very well with the conventional modal model. The effect of having rigid spheres inside the enclosure are then investigated, and it is found that the effect is significant even some distance from the spheres and at frequencies for which the size of the sphere is small compared to a wavelength. Finally the effect of a nonlocally reacting boundary condition is illustrated by assuming that one of the walls of the enclosure is an elastic plate.

Acoustic Analysis of Enclosed Sound Space as well as Its Coupling with Flexible Boundary Structure

“…For comparison, the results obtained based on the superposition of 245 analytical modes are also presented. An excellent comparison between the two predictions is seen over the entire frequency range [16].…”

“…To account for the air absorption, a modal damping ratio η = 0.01 is assumed for each acoustic mode. For a relatively small acoustic damping ratio, the dissipative effect can be accounted for simply through introducing a complex wavenumber k' = k(1 À jξ) [16]. In this method, a complex sound speedc ¼ cð1 À jηÞ is used instead.…”

An equivalent source technique for recovering the free sound field in a noisy environment

“…The basic idea of the ESM is to replace the actual acoustical field by the superposition of the fields produced by a number of equivalent sources placed within a vibrating structure [27][28][29][30][31] or near a measurement surface. 33,34 The strengths of the equivalent sources are determined by matching the boundary condition on the source surface or on the measurement surface.…”

“…The ESM, also named the wave superposition method 27,28 or the source simulation method, 29 is a simple but useful method for solving acoustical radiation, [27][28][29] scattering, 30,31 and NAH problems. 26,[32][33][34] In the ESM, the sound field is approximated by the superposition of the fields created by equivalent sources placed within a vibrating structure or near the measurement surface, and the strengths of the equivalent sources are determined by matching the boundary conditions on the source or on the measurement surface.…”

Review: The Use of Equivalent Source Method in Computational Acoustics

“…Johnson et al 58 used the ESM to calculate the sound field inside an enclosure containing scattering bodies. Bouchet et al 59 used an equivalent sphere for acoustic radiation along with the SVD.…”