Use of elastodynamic reciprocity to analyze point-load generated axisymmetric waves in a plate

Abstract

Elastodynamic reciprocity is used to express wave motion in an infinite elastic layer (plate), due to time-harmonic point-load excitation, as a superposition of Lamb-wave modes. An appropriate orthogonality relation is derived from reciprocity considerations. Elastodynamic reciprocity is also used in conjunction with a dummy wave mode to obtain the coefficients in the wave mode expansion. The specific example is concerned with the response of the layer to a point load normal to the faces of the layer, either applied internally or to one of the faces. It is shown that for normal load applied in the mid-plane of the layer, a limit case of the lowest anti-symmetric mode gives the same result as the Bernoulli-Euler plate theory.