Temporal decay of broadband sound fields in enclosures using a boundary element method

Abstract

A method to predict time-dependent behavior of sound fields in enclosures with diffuse reflection boundaries is described. A boundary element formulation utilizes broadband energy-intensity boundary sources, including propagation time delays. Temporal behavior is expressed in terms of a higher-dimensional eigenvalue/eigenmode problem, with source strength distributions expressed as eigenmodes. A temporal interpolation scheme is used to reexpress the actual delays as a set of integer-multiple delays. The interpolation scheme produces a discrete set of primary eigenvalues and eigenvectors, the total number of which is an integer multiple M of the number of panels N. The value of M is set by the number of interpolation subdivisions of the enclosure wave transit time. For decay from steady-state conditions, the initial value problem involves specifying the initial panel strengths, and M−1 time derivatives of each panel strength set to zero. In temporal decay from steady state, solutions exhibit rapid short-time spatial redistribution of energy, followed by long-time decay of a predominant spatial eigenmode. Long-time decay depends on the behavior of the most slowly decaying eigenmode and the relative source-panel strengths do not depend on initial conditions. Short-time adjustment and decay depends on initial source characteristics and the distribution of wall absorption.