All-frequency normal-mode solution of the three-dimensional acoustic scattering from a vertical cylinder in a plane-horizontal waveguide

Athanassoulis, GA; Belibassakis, KA

dc.contributor.author	Athanassoulis, GA	en
dc.contributor.author	Belibassakis, KA	en
dc.date.accessioned	2014-03-01T01:12:36Z
dc.date.available	2014-03-01T01:12:36Z
dc.date.issued	1997	en
dc.identifier.issn	0001-4966	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12160
dc.subject.classification	Acoustics	en
dc.subject.other	Acoustic wave scattering	en
dc.subject.other	Acoustic wave transmission	en
dc.subject.other	Asymptotic stability	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Boundary value problems	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Frequencies	en
dc.subject.other	Functions	en
dc.subject.other	Integral equations	en
dc.subject.other	Three dimensional	en
dc.subject.other	Azimuthal terms	en
dc.subject.other	Bessel functions	en
dc.subject.other	Dirichlet boundary condition	en
dc.subject.other	Hankel functions	en
dc.subject.other	Neumann boundary condition	en
dc.subject.other	Nondimensional wave number	en
dc.subject.other	Normal mode series	en
dc.subject.other	Ocean acoustic waveguides	en
dc.subject.other	Scattered field	en
dc.subject.other	Underwater acoustics	en
dc.subject.other	acoustics	en
dc.subject.other	amplitude modulation	en
dc.subject.other	analytic method	en
dc.subject.other	article	en
dc.subject.other	geometry	en
dc.subject.other	mathematical computing	en
dc.subject.other	priority journal	en
dc.subject.other	problem solving	en
dc.subject.other	sound transmission	en
dc.subject.other	waveform	en
dc.title	All-frequency normal-mode solution of the three-dimensional acoustic scattering from a vertical cylinder in a plane-horizontal waveguide	en
heal.type	journalArticle	en
heal.identifier.primary	10.1121/1.418295	en
heal.identifier.secondary	http://dx.doi.org/10.1121/1.418295	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	The three-dimensional acoustic scattering from a vertical, impenetrable cylinder in a waveguide is studied. The analytical solution of the problem, for a Dirichlet or a Neumann boundary condition on the scatterer, has been derived recently by Athanassoulis and Prospathopoulos [J. Acoust. Soc. Am. 100, 206-218 (1996)] in the form of a double-infinite normal-mode series, representing the total acoustic field. In order to extend the applicability of this solution to higher frequencies, the total field is decomposed into the incident and the scattered parts. A series expansion for the scattered field is obtained, and the critical parameter controlling its azimuthal convergence is shown to be the nondimensional wave number ka based on the radius a of the cylinder. The general term of the series starts to decay exponentially immediately after the azimuthal index has exceeded the critical value ka, a fact justifying the introduction of the concept of azimuthal- evanescent modes. By exploiting the above decomposition, the direct numerical summation of the normal-mode series becomes feasible up to ka ≃ 1000. For calculations at even higher frequencies (ka→∞), asymptotic expressions are derived by using appropriate integral representations of Bessel and Hankel functions, in conjunction with the method of stationary phase. The asymptotic analysis shows that the scattered field is obtained as a superposition of 2- D point sources lying on the boundary of the vertical cylinder, with appropriate amplitudes and phases. Excellent agreement between asymptotic and direct summation numerical results has been demonstrated, at moderate frequencies, where both representations are expected to be valid.The 3-D acoustic scattering from a vertical impenetrable cylinder in a plane-horizontal waveguide has been studied in the context of normal-mode theory. The analytical solution of the problem, for a Dirichlet or a Neumann boundary condition on the surface of the scatterer, has been derived in the form of a double- infinite series of normal modes representing the total acoustic field. In order to extend the applicability of this solution to higher frequencies, the total field has been decomposed into the incident and the scattered parts, and a series expansion of the scattered field has been derived.	en
heal.publisher	Am Inst Phys, Woodbury, NY, United States	en
heal.journalName	Journal of the Acoustical Society of America	en
dc.identifier.doi	10.1121/1.418295	en
dc.identifier.isi	ISI:A1997XE28800019	en
dc.identifier.volume	101	en
dc.identifier.issue	6	en
dc.identifier.spage	3371	en
dc.identifier.epage	3384	en