Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes

Published

June 1, 2007

Author(s)

J B. Mehl

Abstract

The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a[1-( F(?,f)], where ( is a small scale parameter, the frequency perturbation is calculated to order (2. The formal results apply to acoustic modes whose angular dependence is designated by the indices land m. Specific examples are worked out for the radial (l= 0) and triplet (l= 1) modes, for prolate and oblate spheroids, and for triaxial ellipsoids. The exact eigenvalues for the spheroids, and eigenvalue determined with finite-element calculations, are shown to agree with perturbation theory through terms of order e2. This work is an extension of the author s previouspapers on the acoustic eigenfrequencies of deformed spherical resonators, which were limited to the second-order perturbation for radial modes [J. Acoust. Soc. Am. 71, 1109 1113 (1982)] and the first order-perturbation for arbitrary modes [J. Acoust. Soc. Am. 79, 278 285 (1986)].

Citation

Journal of Research (NIST JRES) -

Volume

112 No. 3

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

acoustic cavity resonators, acoustic eigenvalues, quasispheres, shape pertubation theory

Citation

Mehl, J. (2007), Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed December 16, 2024)