Fast calculations of time-harmonic near field pressure distributions produced by triangular sources

Abstract

An analytical expression is derived for the near field pressure response to a sinusoidal excitation for a triangular piston. The analytical expression eliminates a numerical singularity from the impulse response and therefore achieves much more rapid convergence than the impulse response. This results in shorter computation times relative to the impulse response for a given peak error value. These fast-converging expressions are represented by three integrals, where each integral expression corresponds to an edge of the triangle. Pressure fields are evaluated within a grid that includes the face of the triangular source, and computation times are compared with the impulse response for given values of the peak error. For a specified peak error of 1%, the rapidly converging expressions are at least 50% faster than the impulse response for equilateral triangles with sides ranging from one-half wavelength to 8 wavelengths. For a specified peak error of 10%, the rapidly converging expressions are at least 120% faster than the impulse response when applied to the same group of equilateral triangles. Different reductions in computation time are achieved by other piston and grid geometries.