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International Journal of Engineering Mathematics
Volume 2014 (2014), Article ID 416406, 10 pages
http://dx.doi.org/10.1155/2014/416406
Research Article

Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

Department of Mathematics, Kakatiya University, Andhra Pradesh 506009, Warangal, India

Received 26 December 2013; Accepted 9 March 2014; Published 28 April 2014

Academic Editor: Z.X. Guo

Copyright © 2014 Rajitha Gurijala and Malla Reddy Perati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.