Rayleigh Surface Wave Propagation in Transversely Isotropic Medium with Three-Phase-Lag Model

Document Type: Research Paper

Authors

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, India

Abstract

The present paper is dealing with the propagation of Rayleigh surface waves in a homogeneous transversely isotropic medium .This thermo-dynamical analysis is carried out in the context of three-phase-lags thermoelasticity model. Three phase lag model is very much useful in the problems of nuclear boiling, exothermic catalytic reactions, phonon-electron interactions, phonon scattering etc. The normal mode analysis is employed to obtain the exact expressions of the considered variables. The frequency equations for thermally insulated and isothermal surface in the closed form are derived. Some special cases of frequency equation are also discussed. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. It is found that the results obtained in the present problem agree with that of the existing results obtained by various researchers. This study may find its applications in the design of surface acoustic waves (SAW) devices, structural health monitoring and damage characterization of materials.

Keywords

[1] Rayleigh W.S., 1887, On waves propagating along the plane surface of an elastic solid, Proceedings of the London Mathematical Society 17: 4-11.

[2] Hetnarski R.B., Ignaczak J., 2000, Nonclassical dynamical thermoelasticity, International Journal of Solids and Structures 37: 215-224.

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

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

[5] Hetnarski R. B., Ignaczak J., 1996, Soliton like waves in a low temperature non-linear thermoelastic solid, International Journal of Engineering Science 34: 1767-1787.

[6] Green A.E., Naghdi P. M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31: 189-208.

[7] Tzou D. Y., 1995, A unique field approach for heat conduction from macro to micro scales, Journal of Heat Transfer 117: 8-16.

[8] Roychoudhuri S. K., 2007, On thermoelastic three phase lag model, Journal of Thermal Stresses 30: 231-238.

[9] Abd-Alla A. M., Abo-Dahab S.M., Hammad H.A.H., 2011, Propagation of Rayleigh waves in generalized magneto-thermoelastic orthotropic material under initial stress and gravity field, Applied Mathematical Modeling 35: 2981-3000.

[10] Sharma J. N., Kumar S., Sharma Y.D., 2009, Effect of micro polarity, micro stretch and relaxation times on Rayleigh surface waves in thermoelastic solids, International Journal of Applied Mathematics and Mechanics 5(2): 17-38.

[11] Kumar R., Chawla V., I. A. Abbas, 2012, Effect of viscosity in anisotropic thermoelastic medium with three phase lag model, Journal of Theoretical and Applied Mechanics 39(4): 313-341.

[12] Sharma J. N., Singh H., 1985, Thermoelastic surface waves in a transversely isotropic half space with thermal relaxations, Indian Journal of Pure and Applied Mathematics 16(10): 1202-1212.

[13] Singh B., Kumari S., Singh J., 2014, Propagation of Rayleigh waves in transversely isotropic dual phase lag thermoelasticity, International Journal of Applied Mathematics and Mechanics 10(3): 1-14.

[14] Shaw S., Mukhopadhyay B., 2015, Analysis of Rayleigh surface wave propagation in isotropic micro polar solid under three phase lag model of thermoelasticity, European Journal of Computational Mechanics 24(2): 64-78.

[15] Othman M. I. A., Hasona W. M., Mansour N. T., 2015, The influence of gravitational field on generalized thermoelasticity with two-temperature under three-phase-lag model, Computers, Materials & Continua 45(3): 203-219.

[16] Othman M. I. A., Hasona W. M., Abd-Elaziz E.M., 2015, Effect of rotation and initial stress on generalized micro-polar thermoelastic medium with three-phase-lag, Computational and Theoretical Nanoscience 12(9): 2030-2040.

[17] Othman M. I. A., Zidan M. E. M., 2015, The effect of two temperature and gravity on the 2-D problem of thermoviscoelastic material under three-phase-lag model, Computational and Theoretical Nanoscience 12(8): 1687-1697.

[18] Othman M. I. A., Said S. M., 2014, 2-D problem of magneto-thermoelasticity fiber-reinforced medium under temperature-dependent properties with three-phase-lag theory, Meccanica 49(5): 1225-1243.

[19] Biswas S., Mukhopadhyay B., Shaw S., 2017, Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model, Journal of Thermal Stresses 40: 403-419.

[20] Nowinski J. L., 1978, Theory of Thermoelasticity with Applications, Mechanics of Surface Structures, Sijthoff and Noordhoff International Publishing, Alphen aan den Rijn, Netherlands.