Stoneley signals in perfectly bonded dissimilar thermoelastic half-spaces with and without thermal relaxation

Abstract

The governing equations for each of two perfectly bonded, dissimilar thermoelastic half-spaces include as special cases the Fourier heat conduction model and models with either one or two thermal relaxation times. An exact solution in transform space for the problem of line loads applied in one half-space is obtained. Study of the Stoneley function shows that conditions for existence of roots are more restrictive than in the isothermal case, and that both real and imaginary roots are possible. For the limit case of line loads applied to the interface, an analytical expression for the time transform of the corresponding residue contribution to interface temperature change is derived. Asymptotic expressions for the inverses that are valid for either very long or very short times after loading occurs show that long-time behavior obeys Fourier heat conduction. Short-time results are sensitive to thermal relaxation effects. In particular, a time step load produces a propagating step in temperature for the Fourier and double-relaxation time models, but a propagating impulse for the single-relaxation time model.