Determination of the steady state response of viscoelastically point-supported rectangular anisotropic (orthotropic) plates

In the present study, the steady state response to a sinusoidally varying force applied at the centre of a point-supported anisotropic (orthotropic) elastic plate of rectangular shape is analysed. In doing this, the displacement function of the plate is approximated by using the eigenfunctions of a completely free beam. The difference between the free-end boundary conditions of the plate and the beam is compensated for by considering a differential operator in addition to the governing equation of the plate. Using Galerkin's method, the problem is reduced to the solution of a system of algebraic equations. The influence of the mechanical properties on the made shapes an the steady state response of the viscoelastically point-supported rectangular plates is investigated numerically for a concentrated load at the centre for various values of the mechanical properties characterizing the anisotropy of the plate material. Also, the effect of the location of the point supports is studied. The problems considered are solved within the framework of the Kirchhoff-Love hypothesis. (C) 1998 Academic Press Limited.