Acoustic radiation from random waves on plates

Abstract

Controlling and simulating the sound radiating from complex structures is of importance in many engineering applications. We calculate the radiated acoustic power from plates with diffuse bending vibrations. We characterise the diffuse field by a two-point correlation function (CF) of normal velocities. Given the relation between field–field CFs and ray-dynamical phase space densities, the approach taken here offers a basis for coupling structure borne ray-tracing techniques with acoustic radiation. At the same time, it caters for stochastic, noisy driving of such systems. The results for the radiation efficiency of a plate are presented in an asymptotic form analogous to the Weyl formula for the density of states. Leading contributions from the plate interior and its boundary are derived, with corner corrections also being given for particular boundary conditions and right-angled corners. A notable feature of this analysis is that the bulk contribution vanishes below a critical frequency, and the asymptotic estimate of radiated power then leads with a boundary contribution. This is shown to agree well with a more traditional calculation based on modal analysis in the special case of a rectangular plate.