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Modal Acoustic Force on a Spherical Radiator in an Acoustic Halfspace with Locally Reacting Boundary

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The modal acoustic load on a spherical surface undergoing angularly periodic axisymmetric harmonic vibrations while immersed in an acoustic halfspace with a locally reacting (finite impedance) planar boundary is analyzed in an exact fashion using the classical technique of separation of variables. The solution of the problem is generated by systematically analyzing multi-scattering interaction between the spherical source and the impedance boundary that can be strong or weak depending on their separation, local surface reaction, and frequency. The formulation utilizes the appropriate wave field expansions and a simple local surface reaction framework along with an approximate acoustical wave propagation model involving a complex amplitude spherical wave reflection coefficient which are sensibly applied to simulate the relevant boundary conditions for the given configuration. Incorporation of the classical method of images and the appropriate translational addition theorem permit us to express the acoustic field variables as pairs of double summations in the spherical wave functions, with the coefficients that are coupled through an infinite set of linear complex algebraic equations. These are then truncated and further manipulated to yield the modal impedance matrix and subsequently the modal acoustic force acting on the spherical surface is determined. The analytical results are illustrated with a numerical example in which the spherical surface, excited in vibrational modes of various orders, is immersed near a layer of (locally reacting) fibrous material set on an impervious rigid wall. The obtained data agree well with the approximations given by Morse and Ingard [1] for mechanical impedance of monopole and dipole sources located not very close to the finite impedance plane. The present benchmark solution could eventually be used to validate those found by numerical approximation techniques.
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Document Type: Research Article

Publication date: July 1, 2001

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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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