ASYMMETRIC VIBRATION OF A HEAVILY FLUID-LOADED CIRCULAR PLATE USING VARIATIONAL-PRINCIPLES

As an initial step in the extension of the surface variational principle (SVP) to an assumed modes analysis of vibratory displacement and surface pressure on submerged axisymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers an arbitrary harmonic excitation of an elastic plate. Two configurations, in which the supporting baffle is a thin rigid disk or an infinite plane, are considered. Fourier series expansions of the axismuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonic being governed by equations that are similar in form to those for the analogous axisymmetric problem. Recursion relations using coefficients developed in the course of solving the axisymmetric problem are shown to substantially expedite the evaluation of the additional azimuthal harmonics. Results for a force located at r = a/2 when ka = 3.35, where a is the radius of the plate, are presented in terms of the radial variation associated with each harmonic, as well as overall surface distributions. It is shown that although some of the higher azimuthal harmonics contribute strongly to the surface response, the power radiated in these harmonics is negligible.