The coated thermoelastic body within a low-frequency elastodynamic field

A superposition of a longitudinal and a transverse plane elastic wave excites a small body which is embedded in an infinite elastic medium. The interior of the body exhibits thermoelastic behaviour of the Biot type and it contains a core which is also thermoelastic but with different thermal and elastic parameters. Integral representations for the near as well as the far-field are obtained which involve volume integrals over the shell and the core and surface integrals over the surface of the scatterer and the core–shell interface. Complete low-frequency expansions are provided and the scattering problem is reduced to a sequence of transmission problems for the determination of the coefficients of these expansions. It is shown that the thermal character of the interior media is observed in the low-frequency approximations of order higher or equal to three, when we are close to the scatterer and higher or equal to five, when we are far away from it. Furthermore, the thermoelastic behaviour of the scatterer affects only the radial scattering amplitude, which is of the longitudinal type, while the tangential scattering amplitudes, which are of the transverse type, coincide with the corresponding expressions for scattering by an elastic body with a penetrable elastic core.