An asymptotic formula for sound radiation from plates

We present a new approach to the modelling of sound radiated from vibrating structures that will provide a platform for simulation of larger problems by the method of Dynamical Energy Analysis (DEA), which characterises sound using densities in a ray-dynamical phase space. We consider in particular the radiated acoustic power from plates with diffuse bending vibrations, which we characterise using a two-point correlation function of normal velocities. Such field-field correlation functions are transformed to ray-dynamical phase space densities using a Wigner transformation, which allows insertion into ray-based methods such as DEA. Using correlation functions to characterise plate vibrations also allows the method to cater for stochastic, noisy driving of such systems. The results for the radiation efficiency of a plate are presented in an asymptotic form, with leading contributions from the plate interior and its boundary and 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.