Self and mutual acoustic radiation impedances for two coplanar unbaffled disks

Abstract

The self and mutual acoustic radiation impedances for two coplanar unbafed disks are calculated by using an eigenfunction expansion in terms of oblate spheroidal wave functions. Terms representing outgoing waves from both disks are included. One disk is assumed to be vibrating with a rotationally symmetrical normal velocity distribution, and the other disk is assumed to be stationary. The determination of the expansion coefficients from these boundary conditions is facilitated by the use of an addition theorem which expresses spheroidal wave functions with reference to one coordinate frame in terms of spheroidal wave functions with reference to a second coordinate frame. Numerical results for the special cases where the vibrating disk is either oscillating uniformly or vibrating uniformly on only one side are presented and discussed.