Line input admittance of fluid-loaded wave-bearing layers

Abstract

Exact closed-form expressions givingthe pure-tone input admittance seen by a uniform line force or moment acting on a fluid-loaded thin plate were reported by Crighton [1], with an allusion to the applicability of that result to other wave-bearing layers. The limitations on direct generalizations are explored for plane layers homogeneous in the co-ordinates of the plane. Either the fluids on the two sides of the layer must be identical or one be a vacuum. The layer must be so modelled that the self and mutual spectral admittances, describing dynamic interaction between the driven plane and the wetted surfaces for motions pure in wavenumber on the plane, are rational functions of wavenumber. Some examples are given, including the Timoshenko-Mindlin model of a thick plate and models of plates with compliant layers. Crighton's result is restated in its general form and rederived by standard techniques of contour integration. The analysis is extended to include the effect of dissipation in the fluid and non-uniform distributions of the excitation along the driven line.