Numerical evaluation of the acoustic radiation from planar structures with general baffle conditions using wavelets

A method is presented for computing the acoustic radiation from baffled, unbaffled, or partially baffled planar structures. The surface displacement and the surface pressure are expressed in terms of wavelets, and the acoustic dynamic stiffness (baffled case) or the acoustic receptance (unbaffled case) between any two wavelets is derived in closed form. The wavelets are employed with translation only (i.e., no dilation), and the jinc function is used; the Hankel transform of this function is the Heavyside step function, and this feature greatly simplifies the analysis. There is a trivial mapping between the wavelet amplitudes and the physical motion of the structure, and hence the dynamic stiffness and receptance results can readily be used to derive the acoustic dynamic stiffness matrix (by inverting the receptance matrix in the unbaffled case) in any set of generalized coordinates. Partially baffled systems can then be studied by substructuring the dynamic stiffness matrix. A set of example problems is considered in which the method is used to compute the resistive and reactive radiation efficiency of a range of benchmark systems.