VARIATIONAL FORMULATION OF INTERIOR CAVITY FREQUENCIES FOR SPHEROIDALBODIES

This paper presents interior cavity frequencies for spheroidal bodies in cases of Neumann and Dirichlet homogenous boundary conditions. The Helmholtz wave equation is expressed in terms of prolate spheroidal co ordinates from which a variational formulation is derived for the dete rmination of the interior cavity frequencies. The search of stationari ty is performed by means of a Rayleigh-Ritz type expansion of trial fu nctions. The trial functions are expressed as a double summation of ba sis functions in radial and angular coordinates. A variable transforma tion is applied to the variational form in order to have homogenous bo undary conditions, which are essential for establishing a complete fun ction space of the associated boundary conditions. The present analysi s is verified by comparisons of interior frequencies of a spherical bo dy. of prolate spheroidal bodies, and of the interior characteristic f unctions with the radial and angular functions obtained from prolate s pheroidal differential equations. Interior frequencies are tabulated f or various aspect ratios of spheroidal bodies in accordance with harmo nic orders in azimuthal directions, for both Neumann and Dirichlet con ditions. (C) 1996 Acoustical Society of America.