Line mobilities of infinite plates

Abstract

Analytical solutions are presented for the input mobilities of an isotropic infinite plate with no fluid load. An infinitely long, massless beam is assumed to excite one of the faces of the plate at a fairly low frequency. The plate is described by means of the general equations of motion for three-dimensional elastic bodies, which leads to solutions for the plate that beside bending, longitudinal, and shear waves also incorporate low-frequency Lamb and Love modes. It is shown that the expression for the mobility due to a shear wave excited by an in-line force is similar to that of the mobility due to the longitudinal wave excited by a horizontal force; the only difference is that the shear wave speed is inserted instead of the longitudinal wave speed. It is also shown that, in the case of excitation with a vertical or a horizontal force, the mobilities with respect to the longitudinal waves are much smaller than those connected with the bending waves. An interesting conclusion is that the influence of the Lamb and Love modes is, in general, less important than in the case of point excitation.