Mutual Radiation Impedance between a Circular Piston and a Piston of Arbitrary Shape

Abstract

A time-domain approach is presented to compute the mutual radiation impedance between a circular piston and a piston of arbitrary shape where both pistons are mounted in a rigid planar baffle. The approach is based on numerically evaluating the Fourier transform of an impulse response, which is equivalent to the time-dependent force on the piston of arbitrary shape resulting from the impulsive velocity of the circular piston. An integral expression over a single variable is presented for the impulse response between the circular piston and an arbitrary shaped piston. The mutual impedance between a circular piston and a concentric annular ring is investigated as a special case. A closed-form expression is derived for the impulse response, which is shown to consist of two pulses that are associated with the edges of the ring. Numerical results for the mutual impedance are then presented as a function of frequency and the impedance is shown to be zero for certain critical frequencies. The configuration of two unequal circular pistons is also discussed as a special case, and numerical results are presented for the impulse response and impedance as a function of frequency.