Asymmetric 3D stress- and flux-induced wave propagation in transversely isotropic thermoelastic solids by using of analytical methods

Abstract

Asymmetric 3D wave propagation in transversely isotropic thermoelastic solids is presented by using of potential functions and integral transforms. Governing equations of thermoelastodynamic boundary-value problem (TBVP) are including three equations of motion and an energy equation which make a set of four coupled partial differential equations (PDE) in terms of displacements and temperature. By using of the displacement- and temperature-potential function relationships, four coupled equations of TBVP are reduced to two uncoupled PDEs governing the potential functions which are of sixth and second orders. To solve these uncoupled PDEs, complex Fourier expansions and Hankel integral transforms are used in this paper to suppress the angular and radial variables respectively in cylindrical coordinate system. Consequently, sixth and second order ordinary differential equations (ODE) in terms of depth are received. By solving ODEs, satisfying the radiation and boundary conditions and applying the Hankel inverse transforms, the displacement and temperature functions have been determined in the real space. To validate the analytical and numerical results, some comparisons have been made with the results presented in the literature where excellent agreements have been observed. Important points have been mentioned about speed of SH, SV, P and Rayleigh waves in transversely isotropic and isotropic thermoelastic solids.