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.
