Transient Radiation from Pistons in an Infinite Planar Baffle

Abstract

An approach is presented to compute the near- and farfield transient radiation resulting from a specified velocity motion of a piston in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integral. A simple expression is developed for an impulse response function, which is the time-dependent velocity potential at a spatial point resulting from an impulsive velocity of a piston of any shape. The time-dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the impulse response. Several examples illustrating the usefulness of the approach are then presented. The familiar steady-state nearfield on-axis pressure fluctuations resulting from the sinusoidal velocity of a circular piston is derived from the impulse-response data. The farfield time-dependent radiation from a rectangular piston is also discussed for both continuous- and pulsed-velocity conditions. For a pulsed velocity of time duration T, it is shown that the pressure at several of the field points can consist of two separate pulses of the same time duration.