Acoustic Eigen frequencies in concentric spheroidal-spherical cavities: Calculation by shape per turbation

Kokkorakis, GC; Roumeliotis, JA

dc.contributor.author	Kokkorakis, GC	en
dc.contributor.author	Roumeliotis, JA	en
dc.date.accessioned	2014-03-01T01:13:33Z
dc.date.available	2014-03-01T01:13:33Z
dc.date.issued	1998	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12559
dc.subject	Neumann Boundary Condition	en
dc.subject	Perturbation Method	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.title	Acoustic Eigen frequencies in concentric spheroidal-spherical cavities: Calculation by shape per turbation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1006/jsvi.1997.1445	en
heal.identifier.secondary	http://dx.doi.org/10.1006/jsvi.1997.1445	en
heal.language	English	en
heal.publicationDate	1998	en
heal.abstract	The acoustic eigenfrequencies f(nsm) in concentric spheroidal-spherical cavities are determined analytically, for both Dirichlet and Neumann boundary conditions, by a shape perturbation method. Two types of cavities are examined, one with spheroidal outer and spherical inner boundary and inversely for the other. The analytical determination is possible in the case of small h = d/(2R(2)), (h<<1), where d is the interfocal distance of the spheroidal boundary and 2R(2) the length of its rotation axis. In this case exact, closed form expressions are obtained for the expansion coefficients g(nsm)((2)) and g(nsm)((4)) in the resulting relation f(nsm) (h) = f(ns) (0) [1 + h(2)g(nsm)((2)) + h(4)g(nsm)((4)) + O(h(6))]. Analogous expressions are obtained with the use of the parameter v = 1 -(R-2/R-2')(2), (\v\ << 1) where 2R(2)' is the length of the other axis of the spheroidal boundary. There is no need for using any spheroidal wave functions and the expansion formulas connecting them with the concentric spherical ones. The pressure field is expressed in terms of spherical wave functions, while the equation of the spheroidal boundary is given in terms of the spherical co-ordinates. Numerical results are given for various values of the parameters. (C) 1998 Academic Press Limited.	en
heal.publisher	ACADEMIC PRESS LTD	en
heal.journalName	Journal of Sound and Vibration	en
dc.identifier.doi	10.1006/jsvi.1997.1445	en
dc.identifier.isi	ISI:000073690200010	en
dc.identifier.volume	212	en
dc.identifier.issue	2	en
dc.identifier.spage	337	en
dc.identifier.epage	355	en