FORCED VIBRATION ANALYSIS OF ISOTROPIC THIN RECTANGULAR PLATES

Abstract

This work used the general shape function assumed by Szilard (2004) to formulate the solution to the forced vibration equation of an isotropic thin rectangular plate. By applying the appropriate boundary conditions on dimensionless co-ordinates (ζ, η) it produced the shape function of a rectangular plate with opposite edges clamped, one edge of the other opposite edges clamped, and the other edge is simply supported, this is denoted as ‘CCSC’ plate, in terms of a deflection constant, A. It converted the forced vibration equation to an energy equation by multiplying it with a deflection term, w, and integrating over the whole surface of the plate. By substituting the shape function and aspect ratio of the plate into the energy equation, the value of A was obtained, from which the full deflection equation was derived. Then the shear force, deflections, bending and twisting moments were obtained from the deflection equation. The values of deflections and bending moments obtained satisfy the natural and geometric boundary conditions of the plate.