Wave propagation in an incompressible transversely isotropic thermoelastic solid

Abstract

In the present paper, the equations of motion and heat conduction equation of an incompressible transversely isotropic thermoelastic solid are formulated in view of Lord and Shulman theory on generalized thermoelastcity. The equations of motion and heat conduction equation reduce to two coupled equations in temperature and a scalar function depending on displacement. Plane harmonic solution of these coupled equations shows the existence of two homogeneous plane waves. These coupled equations are also solved for surface wave solutions which satisfy the required radiation conditions in the half-space. The surface wave solutions satisfy the appropriate boundary conditions at traction-free thermally insulated or isothermal surface of half-space and a secular equation of Rayleigh wave speed is obtained for thermally insulated case and isothermal case. For thermally insulated case, the numerical values of non-dimensional speed of Rayleigh wave are computed by using Iteration method. The wave speeds of plane waves and Rayleigh wave are illustrated graphically to observe the effects of transverse isotropy, material constants, frequency, angle of propagation and thermal relaxation in time.