Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

Rajitha Gurijala,Malla Reddy Perati

doi:10.1155/2014/416406

Rajitha Gurijala, Malla Reddy Perati

Open Access

https://doi.org/10.1155/2014/416406

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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.

Highlights

In day-to-day problems, composite structures play an important role
We investigate the axially symmetric vibrations of composite poroelastic spherical shell in the framework of Biot’s theory
In the framework of Biot’s theory, axially symmetric vibrations of composite poroelastic spherical shell are investigated in the case of both pervious and impervious surfaces

Summary

Introduction

In day-to-day problems, composite structures play an important role. The term composite is applied to materials that are created by mechanically bonding two or more different elastic materials together. Kumar [1] studied the axially symmetric vibrations of fluid-filled spherical shells employing three-dimensional equations of linear elasticity. For torsional vibrations of solid prolate spheroids and thick prolate spheroidal shells, frequency equations and mode shapes are presented in analytic form [2]. In the paper in [6], radial and rotatory vibrations of fluid-filled and empty poroelastic spherical shells are investigated. Some structures may be far from their center of curvature and thickness might be very small when compared to radii of curvature In this case, we have ring modes [8]. We investigate the axially symmetric (independent of azimuthal coordinate) vibrations of composite poroelastic spherical shell in the framework of Biot’s theory.

Governing Equations and Solution of the Problem

Boundary Conditions and Frequency Equations

Poroelastic Thick Walled Hollow Spherical Shell: A Particular Case

It is found that

Numerical Results

Conclusion