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Acoustic Scattering by an Elliptic Cylindrical Absorber

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This study treats the two-dimensional interaction of a plane sound wave with an air-saturated porous elastic cylinder of elliptic cross section suspended in an unbounded ideal acoustic medium. The novel features of Biot dynamic theory of poroelasticity along with the classical method of Eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an air-saturated cylindrical plastic foam absorber is insonified by a plane sound wave at selected angles of incidence. The most important acoustic field quantities such as backscattering form function amplitude, total scattering cross section, and total power scattered are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and cross sectional ellipticity in addition to poroelastic absorption effects are examined. Limiting cases involving an elastic elliptic cylinder and also a circular fluid cylinder in an ideal fluid are considered and fair agreements with recent investigations are obtained.
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Document Type: Research Article

Publication date: September 1, 2007

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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