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Lookup NU author(s): Dr Barry Gallacher, Emeritus Professor James Burdess
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Copyright © 2026 by ASME.It is shown that a circular acoustic cavity bounded by a set of circular reflector grooves and formed from elastically isotropic material can support degenerate resonant behavior for circular wave-fronted Rayleigh waves. The Rayleigh wave response to a time-harmonic, circular line-load possessing both in-plane and out-of-plane components, located within a circular acoustic cavity, is determined. The forced response is expressed in terms of the family of Bessel functions whose order is determined by the cyclic order of the circular line-load. A multiple-scale perturbation method is applied to the homogenized equations of motion and boundary conditions. It is shown that significant cumulative reflection of the circular wave-fronted Rayleigh waves from the reflective array can occur and that the axisymmetric design satisfies the conditions for degenerate resonance. Thus, the resonator has potential application as a Coriolis gyroscope. The perturbation/homogenization method of analysis shows that the zero-order solution in the array is affected at the first order by periodic irregularities at approximately half the wavelength of the incident Rayleigh wave and that the form of the surface is similar in this respect to that of the conventional 1D Rayleigh resonator. The Q-factor of the resonator is calculated and is expressed in terms of the wavenumber defining the reflective array. It is shown that the Q-factor depends exponentially on the radial length of the reflective array. For the geometry considered, a Q-factor of 21,000 is shown to be possible.
Author(s): Gallacher BJ, Burdess JS
Publication type: Article
Publication status: Published
Journal: Journal of Applied Mechanics
Year: 2026
Volume: 93
Issue: 10
Online publication date: 28/07/2026
Acceptance date: 28/06/2026
ISSN (print): 0021-8936
ISSN (electronic): 1528-9036
Publisher: American Society of Mechanical Engineers (ASME)
URL: https://doi.org/10.1115/1.4072302
DOI: 10.1115/1.4072302
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