Oscillations of plates under the action of concentrated loads in an acoustic medium

Abstract

Abstract Steady-state oscillations induced by concentrated forces acting on infinite isotropic and orthotropic plates in contact with a liquid are considered. On the basis of an asymptotic integration of the equations, an approximation method for solving the problem is proposed. Explicit expressions are obtained for the first approximations of deflections of the plates and the acoustic pressure in the medium. In the case of an isotropic plate, numerical integration of the equations in an exact formulation is also carried out and a comparison with the approximate analytic solution given. The isotropic plate problem has been previously considered /1–4/.Our study complements these results, and makes it possible to break up the initial problem into several simpler problems and to identify the structure of the integrals and simplify the solution method. As a result we are able to generalize our method to boundary value problems. A solution of the orthotropic plate problem (which has not previously been considered) is obtained.