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Mechanics of Composite Materials

, Volume 48, Issue 4, pp 449–466 | Cite as

Acoustic conductance of an anisotropic spherical shell submerged in a liquid 1. Wave model of contact interaction between a solid hollow sphere and a liquid. Degenerate solutions

  • V. A. Polyakov
Article

With the example of a thick-walled spherical shell made of an anisotropic material, the decrease in the vibration intensity across the thickness of shells related to a change in the amplitude of wave propagation is considered. The motion rate of the outer surface of the shell, contacting a liquid medium, as a function of shell thickness and material properties in the circumferential and radial directions is investigated by using a model of radial vibrations caused by a harmonic source located on the inner surface of the shell. The model takes into account the interaction of surface of the shell with the surrounding medium. By using the operational method, with the use of the Laplace transformation, a general solution to the wave problem for radial vibrations is obtained. The amplitude solution is found in an expansion form with the use of the theory of residues. The degenerate solution of the transcendental equation for eigenfrequencies, which, in the general case, is a combination of Bessel functions, is investigated in the cases where the radial and circumferential elastic moduli differ considerably.

Keywords

spherical shell radial vibrations transversely isotropic material eigenfrequencies Laplace operational method complex analytical solution in residues 

Notes

Acknowledgments

The author is grateful for the financial and advisory support rendered to the investigation within the framework of the ERAF project, No. 2010/0290/2DP/2.1.1.1.0/10/APIA/VIAA/053.

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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Institute of Polymer of MechanicsUniversity of LatviaRigaLatvia

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