Wave motion in an isotropic elastic layer generated by a time-harmonic point load of arbitrary direction

Abstract

Wave motion in an infinite elastic layer due to the application of a time-harmonic point load of arbitrary direction, applied either internally or on one of the faces of the layer, is expressed as a sum of four expansions in Lamb-wave modes and horizontally polarized wave modes. The point load is decomposed into components normal and parallel to the plate faces. Each of these cases is decomposed into a symmetric and an antisymmetric loading case, relative to the mid-plane of the layer. The displacement solutions for the symmetric and antisymmetric cases are expressed as expansions of symmetric and antisymmetric modes, respectively. Appropriate orthogonality relations are derived from reciprocity considerations. Elastodynamic reciprocity is also used in conjunction with dummy wave modes to obtain the coefficients in the wave-mode expansion.