Abstract
The effects of imperfect spherical shape on the modes of a spherical acoustic resonator are considered. The resonator boundary is described by a series of spherical harmonics r=a+εa∑ clkYlk, where ε is a small parameter. It is convenient to summarize the results by considering deformations which do not change the resonator volume. Earlier work showed, for pure radial modes subject to axisymmetric shape perturbations, that the fractional shift of the resonance frequency is proportional to ε2. This work extends this result to arbitrary shape perturbations. Nonradial modes, for which the acoustic pressure is proportional to jn (kns r) Ynm (θ, φ) with n≥1 are (2n+1)-fold degenerate for a perfect spherical resonator. Deformation of the resonator normally shifts the resonance frequencies by an amount which is linear in ε. However, the average shift of a degenerate set of modes with indices {ns} is of order ε2. Axisymmetric shape perturbations normally reduce the degeneracy of the nonradial modes to (n+1)-fold, and arbitrary deformations normally lift the degeneracy completely. The modes with indices {ns} are sensitive only to the terms clk with even values of l in the range l≤zn. A formalism for quantitative estimates is developed. Numerical results are obtained for some n=1 and n=2 cases.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
