Energy exchange in uncorrelated ray fields of vibroacoustics

Abstract

This paper is concerned with the basic equations governing energy and intensity in incoherent ray fields. Some fictitious sources are distributed on the boundary of the domain but also on diffracting wedges and peaks. Their powers are determined by some appropriate boundary integral equations. Once these powers are known, energy and intensity inside the domain are given by a simple superposition of contributions of these sources. All paths of propagation are taken into account including direct, reflected, refracted, transmitted, and diffracted rays, but also, radiation by surface, edge or corner modes, and the reciprocal paths for structural response. This theory unifies several fields from the "radiosity method" in room acoustics which determines the reverberation time to the "radiative transfer method" in structural dynamics which gives the repartition of vibrational energy inside subsystems of built-up structures. This is therefore a candidate for an alternative to statistical energy analysis when fields are nondiffuse.

Discrete flow mapping: transport of phase space densities on triangulated surfaces

“…The disadvantage of these methods is that the underlying assumptions are often hard to verify a priori or are only justified when an additional averaging over 'equivalent' subsystems is considered. The shortcomings of SEA have been addressed by Langley [22], Langley & Bercin [23] and more recently in a series of papers by Le Bot [24][25][26]. A computational method called dynamical energy analysis (DEA), which is based on an FPoperator approach, has been introduced by Tanner [27] and further developed in Chappell et al [28].…”

“…The disadvantage of these methods is that the underlying assumptions are often hard to verify a priori or are only justified when an additional averaging over 'equivalent' subsystems is considered. The shortcomings of SEA have been addressed by Langley (1992), Langley & Bercin (1994) and more recently in a series of papers by Le Bot (1998Bot ( , 2002Bot ( , 2006.…”

High frequency vibroacoustics: A radiative transfer equation and radiosity based approach

“…The development of the radiosity method in acoustics and its application to sound illumination problem in room acoustics or reverberation time determination beyond the validity of Sabine's law underline its importance in engineering. Furthermore, its extension to specular reflection and diffraction highlights that it may be also useful in a larger class of problems, including sound radiation, structural response, sound transmission [57]. From this point of view, radiative exchange equations look like an a t u r a le x t e n s i o no fs t a t i s t i c a le n e r g ya n a l y s i sw h e ne n e r g yfi e l d sa r en o t diffuse.…”

A boundary integral formalism for stochastic ray tracing in billiards

“…One such formulation is given by the rendering equation [4] which has its origins in computer graphics, but has been applied more widely since [16,17].…”