Two nonmixed symmetric end-loadings of an elastic waveguide

Abstract

This investigation treats the response of the semi-infinite plate with free faces subjected to suddenly applied normal loads on its end. The plate is elastic and in plane strain. The normal loads are symmetric and act in the absence of shear stress, i.e. the plate has nonmixed end conditions. A double Laplace transform technique is used to obtain long-time information for two particular normal loads; the uniform load and the line-load. Near-field and far-field approximations are found. Results in the long-time near-field for the uniform load reduce to elementary forms; for the line-load however, the corresponding forms are quite complex entailing singular terms and some numerically evaluated contributions. The far-field approximations give rise to integral of the Airy function forms for both loads and, if the forces applied under the two loadings are equal, these far-field responses are shown to be identical.