Radial Vibration Of a Non-Homogeneous Anisotropic Elastic Spherical Shell With Inclusion


Sudipta Sengupta,Indrajit Roy,H.S. Chakraborty,




spherical shell,anisotropic elasti ,radial vibration ,elastic inclusion,


The aim of this paper is to study the radial vibration of a non-homogeneous sherically anisotroplc elastic spherical shell with an isotropic elastic inclusion as the core. The non-homogeneous of the material is characteised by taking linear vibration with radial distance of elastic parameters and mass density. This property of non-homogeneity is assumed to be satisfied by the entire shell of the sphere, while the core of the spherical shell behaves like an inclusion of isotropic homogeneouselastic mass. Satisfying the appropriate boundary conditions, the frequency of vibration of the composite solid sphere has been determined. results obtained by other authors may be deduced from our more general result as special cases.


I. A.E.H. Love , A treatise on the Mathematical theory of Elasticity, Dover publication.(1952).

II. A.E.H. Love, Some problem of Geodynamics, Cambridge University pPress, London.(1911).

III. R.F.S. Hearmon, An Introduction to Applied Anisotropic Elasticity, Oxford University Press, London.(1961).

IV. S.G. Lekhnitski, Theory of Elasticity of an Anisotropic elastic body. Holden Day Inc.(1963).

V. W. Olszak, non-homogeneous in Elasticity and Plasticity-Proceeding of the Internal Union of Theoretical and Applied Mechanics Symposium, pergamon press.

VI. P.R. Sengupta, Problem of twised elastic sphere with a concentric inhomogeneous spherical inclusion, Jour. Sci. Engg. Res. Vol-8, No-2, pp.193-203 (1964).

VII.P.R. Sengupta, Inclusion in elastic solids of work-hardening materil, Ind. Jour. Mech. & Math. Part-II, Special Issue. pp.80-89 (70th birth anniversasry volume of Prof. B.Sen, F.N.A.) (1969).

VIII.P.R. Sengupta, & A.N. Basumallick, Radial deformation of a non-homogeneous spherically anisotropic elastic sphere with a concentric spherical inclusion, Ind. Jour. Mech. & Math, Vol-8, No-2, pp.1-9(1970).

IX. J.G. Chakraborty, radial and rotatory vibration of a spherical shell of aeolotropic elastic material, Bull. Soc. Vol-47, No.4 (1965).

X. S.P. Sur, Radial and rotatory vibration of a sphere of non-homogeneous spherically aeolotropic material of unifrom density. Ind. Jour. Mech. Math. Vol-II, No.1 (1964).

XI. P.R. Sengupta & S.K. Roy, Radial vibration of a sphere of general viscoelastic solid, Gerlands Beitr. Geophysik, Leipzig, 92, 5, s.435-442 (1983).

XII. P.R. Sengupta & S.K. Roy, Rotatory vibration of a sphere of general viscoelastic solid, Gerlands Beitr. Geophysik, Leipzig, 92, 1, s.70-76 (1983).

XIII. H.M. Youssef, dependence of modulus of elasticity and thermal conductivity on reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity, Appl. Math. Mech., 26, 4,pp.470-475. (2005).

XIV. S. Banerjee & S.K. Roy Chowdhury, Spherically symmetric thermo-visco-elastic waves in a visco-elastic medium with a spherical cavity, Computers Math. Applic., 30,1, pp.91-98. (1995).

XV. M.Rakshit & B. Mukhopadhyay: An electro-magneto-thermo-visco-elastic problem in an infinite medium with a cylindrical hole, Int. J. Eng. Sci., 43, pp.925-936, (2005).

XVI. M.A.Ezzat.Fundamental solution in generalized magneto-thermoelasticity with two relaxation times for parfact conductor cylindrical region, Int. J. Eng. Sci., 42, pp.1503-1519, (2004).

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