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Free Vibrations of a Spherically Isotropic Hollow Sphere

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In this paper an exact analysis of the nonaxisymmetric vibrations of an aeolotropic hollow sphere is presented. It is found that, as in the case of an isotropic sphere, there are two independent classes of vibrations, viz., the first and second class. In the radial coordinate, the solution for the vibration of the first class is given in terms of Bessel functions, while the solution for the vibration of the second class is obtained using a Frobenius power series. Numerical results are presented giving the lower mode frequencies for different values of sphere thickness to radius ratio, for a variety of spherically isotropic materials. These results are compared with corresponding results predicted on the basis of a shell theory.
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Document Type: Research Article

Publication date: June 1, 1972

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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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