The impulse response and mutual radiation impedance between a circular piston and a piston of arbitrary shape

Abstract

An approach is presented to compute the time-dependent force on a piston of arbitrary shape which results from the specified velocity of a circular piston in a rigid planar baffle. The force is expressed as the convolution of the specified piston velocity with an impulse response which is equivalent to the time-dependent force on the piston of arbitrary shape that results from an impulsive velocity of the circular piston. The mutual radiation impedance is shown to be equivalent to the Fourier transform of the impulse response. A circular piston and concentric annular ring are then investigated using the approach. A closed-form expression for the impulse response is presented and the impulse response is shown to consist of two pulses, each of which is associated with an edge of the ring. Numerical results are presented to illustrate the effect of changing the relative size of the piston and ring on the impulse response and mutual radiation impedance. Several interesting characteristics of the mutual radiation impedance are discussed and are shown to be in agreement with those obtained from an approximate solution.