The vibrations of a bounded plate in a fluid

Abstract

An approximate analytic method is proposed to solve boundary vlaue problems for the harmonic oscillations of a bounded plate in contact with a fluid. The procedure for constructing the successive approximations is such that the first approximation will describe the solution in the main, while subsequent approximations reduce to small refinements on the first approximation. The method is realized in solving a model problem on the plane vibrations of a plate, a strip in a rigid screen with unilateral contact with a liquid medium. Results of a numerical solution of the problem are presented in addition to the approximate analytic solution. By comparing these solutions one can estimate the error of the analytic method in determining the resonance frequencies and modes of plate vibrations in a fluid. This problem has been examined earlier in a somewhat different formulation; the most complete account of the results and bibliographic information can be found in /1/.