The Time-Dependent Force and Radiation Impedance on a Piston in a Rigid Infinite Planar Baffle

Abstract

An approach is presented to compute the time-dependent force acting on a piston in a rigid infinite planar baffle as a result of the specified velocity of the piston. The approach to computing the force is applicable to both sinusoidal and nonsinusoidal velocity pulses and is valid for all piston shapes. The approach, which is based on a Green's-function solution to the time-dependent boundary value problem, utilizes a transformation of coordinates to simplify the evaluation of the double surface integrals. An impulse response function is defined such that the time-dependent force can be obtained by differentiating the convolution of the impulse response and piston velocity time functions. A closed-form expression for the impulse response of a circular piston is derived and discussed. Numerical results for the impulse response and the forces on large square pistons resulting from sinusoidal piston velocities are then presented and discussed to compare the transient and steady-state behavior of the forces. Finally, an approach is presented to compute the radiation impedance as a function of normalized frequency from the impulse response data, and the approach is used to obtain the normalized radiation resistance and reactance for square pistons.