Rayleigh Waves in a Homogeneous Magneto-Thermo Voigt-Type Viscoelastic Half-Space under Initial Surface Stresses

Document Type: Research Paper

Author

Faculty of Engineering & Technology, GNA University, Phagwara, India, 163, Chotti Baradari, Phase-1, Garah Road, Jalandhar-144022, India

Abstract

This paper deals with the propagation of magneto-thermo Rayleigh waves in a homogeneous viscoelastic half-space under initial stress. It has been observed that velocity of Rayleigh waves depends on viscosity, magnetic field, temperature and initial stress of the half-space. The frequency equation for Rayleigh waves under the effect of magnetic field, stress and temperature for both viscoelastic and elastic medium is first obtained by using classical theory of thermoelasticity and then computed numerically. The variation of phase velocity of Rayleigh waves with respect to initial hydrostatic stress in viscoelastic and elastic half-space is shown graphically. In the absence of various parameters of the medium, the obtained results are in agreement with classical results given by Caloi and Lockett. 

Keywords

[1] Lockett F.J., 1958, Effect of thermal properties of a solid on the velocity of Rayleigh waves, Journal of the Mechanics and Physics of Solids 7(1): 71-75.
[2] Caloi P., 1950, Comportement des ondes de Rayleigh dans un milieu firmo-´elastique ind´efini, Publications du Bureau Central Séismologique International: Travaux Scientifiques Série A 17: 89-108.
[3] Biot M.A., 1965, Mechanics of Incremental Deformations Theory of Elasticity and Viscoelasticity of Initially Stressed Solids and Fluids, Including Thermodynamic Foundations and Applications to Finite Strain, JohnWiley & Sons, New York.
[4] Nowacki W., 1962, Thermoelasticity, Addison-Wesley, London.
[5] Addy S.K., Chakraborty N., 2005, Rayleigh waves in a viscoelastic half-space under initial hydrostatic stress in presence of the temperature field, International Journal of Mathematics and Mathematical Sciences 24: 3883-3894.
[6] Sethi M., Gupta K.C., Rani M., Vasudeva A.., 2013, Surface waves in homogenous visco-elastic media of higher order under the influence of surface stresses, Journal of the Mechanical Behavior of Materials 22: 185-191.
[7] Singh B., Bala K.., 2013, On Rayleigh wave in two-temperature generalized thermoelastic medium without energy dissipation, Applied Mathematics 4(1): 107-112.
[8] Vinh P.C., 2009, Explicit secular equations of Rayleigh waves in elastic media under the influence of gravity and initial stress, Applied Mathematics and Computation 215(1): 395-404.
[9] Kakar R., Kakar S., 2013, Rayleigh waves in a non-homogeneous, thermo, magneto, prestressed granular material with variable density under the effect of gravity , American Journal of Modern Physics 2(1): 7-20.
[10] Abd-Alla A.M., Abo-Dahab S.M., Bayones F.S., 2011, Rayleigh waves in generalized magneto-thermo-viscoelastic granular medium under the influence of rotation, gravity field, and initial stress, Mathematical Problems in Engineering 2011:1-47.