Abstract
We consider an incident time harmonic longitudinal or transverse plane wave which propagates in an infinite isotropic and homogeneous elastic medium and it is scattered by a penetrable body containing an impenetrable core. Integral representations for the total displacement field as well as the normalized scattering amplitudes are provided. A systematic procedure for finding the low-frequency expansions for the displacement field, the scattering amplitudes and the scattering cross section is developed. As a result the scattering problem is reduced to a sequence of elastostatic problems which can be solved using the Papkovich-Grodski-Neuber potentials. The leading low-frequency terms of the scattering amplitudes and the cross section are evaluated. The proposed procedure is applied to the scattering of a plane elastic wave by a penetrable spherical scatterer with a concentric spherical rigid inclusion. Particular values of the physical parameters correspond to special scattering problems and they are included as such.
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