This is a longer version of the paper I was invited to give at the Acoustics08 conference in Paris. In this paper I present a method for improving the convergence in the frequency domain of the mutual interaction impulse response functions for an array of Sonar transducers. This allows the mutual interaction impulse response functions to be computed efficiently by Fourier transforming a modified frequency response.

The Kirchhoff integral equation in acoustics involves delayed or retarded values of the surface pressure, the time derivative of surface pressure, and the normal acceleration. The numerical solution of Kirchhoff's equation reduces to a time recursion relation for the surface pressures. It turns out that there are stability problems associated with the solution of Kirchhoff's equation when the time step is too small. A numerical technique is presented in this paper that greatly improves the stability.

In this paper I describe a technique for calculating the far-field pressure due to a vibrating piston of arbitrary shape located on an infinite rigid planar baffle. The technique is based on a two-dimensional version of Green's theorem. Integral expressions over the area of the piston are converted to line integrals around the perimeter of the piston. Explicit relations are derived for polygonal pistons with any number of sides.

Oscar Lindeman in a 1974 JASA article [Lindeman, Oscar, Transient fluid reaction on a baffled plane piston of arbitrary shape, J. Acoust. Soc. Am., 55, No. 4, April 1974] presented a technique for obtaining the self radiation impedance of a baffled piston on a plane as a Fourier transform of its impulse response. The impulse response was expressed as a double contour integral around the pistons perimeter. This technique has been applied by a number of authors to pistons of various shapes. In this paper I will illustrate how Lindeman's technique can be extended to the mutual acoustic interaction between two pistons of arbitrary shape on a rigid planar baffle.

Additional papers are referenced in the document Modeling of Sonar Transducers and Arrays (pdf).