problem of rayleigh wave propagation in thermoelastic diffusion

In this work, the problem of rayleigh wave propagation is considered in the context of the theory of thermoelastic diffusion. the formulation is applied to a homogeneous isotropic thermoelastic half space with mass diffusion at the stress free, isothermal, isoconcentrated boundary. using the potential functions and harmonic wave solution, three coupled dilatational waves and a shear wave is obtained. after developing mathematical formulation, the dispersion equation is obtained, which results to be complex and irrational. this equation is converted into a polynomial form of higher degree. the roots of this polynomial equation are verified for not satisfying the original dispersion equation and therefore are filtered out and the remaining roots are checked with the property of decay with depth. phase velocity and attenuation coefficient of the rayleigh wave are computed numerically and depicted graphically. behavior of particle motion of these waves inside and at the surface of the thermoelastic medium with mass diffusion is studied. some particular cases are also deduced from the present investigation.