Effect of Rotation and Stiffness on Surface Wave Propagation in a Elastic Layer Lying Over a Generalized Thermodiffusive Elastic Half-Space with Imperfect Boundary

Subject Areas : Engineering

R Kumar ¹ , V Chawla ²

1 - Department of Mathematics, Kurukshetra University
2 - Department of Mathematics, Kurukshetra University

Received: 2009-12-17 Accepted : 2010-04-18 Published : 2010-03-30

Keywords: Phase velocity, Attenuation coefficient, Specific loss, Isotropic, Generalized thermoelastic diffusion, Stiffness, Amplitude, Rotation,

Abstract :

The present investigation is to study the surface waves propagation with imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of Green-Lindsay (G-L model) theory. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed at the free plane boundary. Specific loss of energy is obtained and presented graphically. The effects of rotation on phase velocity, attenuation coefficient and amplitudes of displacements, temperature change and concentration are depicted graphically. Some Special cases of interest are also deduced and compared with known results.

References:

[1] Achenbaeh J.D., Zhu H., 1989, Effect of interfacial zone on mechanical behaviour and failure of reinforced composites, Journal of the Mechanics and Physics of. Solids 37: 381-393.

[2] Aouadi M., 2006, Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion, ZAMP, Zeitschrift für angewandte Mathematik und Physik 57(2): 350-366.

[3] Aouadi M., 2006, A generalized thermoelastic diffusion problem for an infinitely long solid cylinder, International Journal of Mathematics and Mathematical Sciences 2006: 1-15.

[4] Aouadi M., 2007, A problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 44: 5711-5722.

[5] Benveniste Y., 1984, The effective mechanical behavior of composite materials with imperfect contact between the constituents, Mechanics of Materials 4: 197-208.

[6] Benveniste Y., 1999, On the decay of end effects in conduction phenomena: A sandwich strip with imperfect interfaces of low or high conductivity, Journal of Applied Physics 86: 1273-1279.

[7] Bullen K.E., 1963, An Introduction of the Theory of Seismology, Cambridge University Press, Cambridge.

[8] Dawn N.C., Chakraborty S.K., 1988, On Rayleigh waves in Green-Lindsay’s model of generalized thermoelastic media, Indian Journal of Pure and Applied Mathematics 20(3): 276-283.

[9] Dudziak W., Kowalski S.J., 1989, Theory of thermodiffusion for solids, International Journal of Heat and Mass Transfer 32: 2005-2013.

[10] Ewing W.M., Jardetzky W.S., Press F., 1957, Elastic Layers in Layered Media, McGraw-Hill Company, Inc., New York, Toronto, London.

[11] Green A.E., Lindsay K.A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.

[12] Hashin Z., 1990, Thermoelastic properties of fiber composites with imperfect interface, Mechanics of Materials 8: 333-348.

[13] Hashin Z., 1991, The spherical inclusion with imperfect interface, ASME Journal of Applied Mechanics 58: 444-449.

[14] Hetnarski R.B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451-476.

[15] Kolsky H., 1963, Stress Waves in Solids, Clarendon Press Oxford, Dover Press, New York.

[16] Kumar R., Kansal T., 2008, Propagation of Rayleigh waves on free surface in transversely isotropic thermoelastic diffusion, Applied Mathematics and. Mechanics 29(11): 1451-1462.

[17] Kumar R., Kansal T., 2008, Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate, International Journal of Solids and Structures 45: 5890-5913.

[18] Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of. Solids 15: 299-309.

[19] Nowacki W., 1974, Dynamical problem of thermoelastic diffusion in solid–1, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 55-64.

[20] Nowacki W., 1974, Dynamical problem of thermoelastic diffusion in solid-11, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 129-135.

[21] Nowacki, W., 1974. Dynamical problem of thermoelastic diffusion in solid-111, Bulletin of Polish Academy of Sciences Series, Science and Technology 22: 275-276.

[22] Nowacki W., 1974, Dynamic problems of thermo- diffusion in elastic solids, Proceedings of Vibration Problems 15, 105-128.

[23] Olesiak Z.S., Pyryev Y.A., 1995, A coupled quasi-stationary problem of thermodiffusion for an elastic cylinder, International Journal of Engineering Science 33(6): 773-780.

[24] Pan E., 2003, Three-dimensional Green’s function in anisotropic elastic bimaterials with imperfect interfaces, ASME Journal of Applied Mechanics 70: 180-190.

[25] Sharma J.N., Walia V., 2007, Effect of rotation on Rayleigh waves in transversely isotropic piezoelectric materials, Journal of Sound and Vibration 44: 1060-1072.

[26] Sharma J.N., Walia V., 2008, Effect of rotation and thermal relaxation on Rayleigh waves in piezoelectric half-space, International Journal of Mechanical Sciences 50: 433-444.

[27] Sherief H.H., Hamza F.A., Saleh H.A., 2004, The theory of generalized thermoelastic diffusion, International Journal of Engineering Science 42: 591-608.

[28] Sherief H.H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures 42: 4484-4493.

[29] Singh B., 2005, Reflection of P and SV waves from free surface of an elastic solid with generalized thermoelastic diffusion, Journal of Earth System Science 114(2): 159-168.

[30] Singh B., 2006, Reflection of SV wave from free surface of an elastic solid in generalized thermoelastic diffusion, Journal of Sound and Vibration 291(3-5): 764-778.

[31] Yu H.Y., Wei Y.N., Chiang F.P., 2002. Lord transfer at imperfect interfaces dislocation--like model, International Journal of Engineering Science 40: 1647-1662.

[32] Yu H.Y., 1998, A new dislocation-like model for imperfect interfaces and their effect on load transfer, Composites A 29: 1057-1062.

[33] Zhong Z., Meguid S.A., 1996, On the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface, ASME Journal of Applied Mechanics 63: 877-883.