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- W2034649991 abstract "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 coordinates from which a variational formulation is derived for the determination of the interior cavity frequencies. The search of stationarity is performed by means of a Rayleigh–Ritz type expansion of trial functions. The trial functions are expressed as a double summation of basis functions in radial and angular coordinates. A variable transformation is applied to the variational form in order to have homogenous boundary conditions, which are essential for establishing a complete function space of the associated boundary conditions. The present analysis is verified by comparisons of interior frequencies of a spherical body, of prolate spheroidal bodies, and of the interior characteristic functions with the radial and angular functions obtained from prolate spheroidal differential equations. Interior frequencies are tabulated for various aspect ratios of spheroidal bodies in accordance with harmonic orders in azimuthal directions, for both Neumann and Dirichlet conditions." @default.
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- W2034649991 date "1996-11-01" @default.
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- W2034649991 title "Variational formulation of interior cavity frequencies for spheroidal bodies" @default.
- W2034649991 doi "https://doi.org/10.1121/1.417110" @default.
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