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, 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 resultant surface integrals. An impulse response function is defined as a function of a single surface integral. The time-dependent force can then be obtained by differentiating the convolution of the impulse-response and piston-velocity time functions. The approach to compute the force is applicable for both sinusoidal and nonsinusoidal velocity pulses and is valid for all piston shapes. Numerical results for the impulse response and forces on square pistons resulting from sinusoidal piston velocities are then presented and discussed. Finally, an approach is presented to compute the radiation impedance as a function of normalized frequency from the impulse response data. The approach, which is based on sampling theory, is used to obtain the normalized radiation resistance and reactance for square pistons. The results are then compared to those of earlier investigators.