3-DIMENSIONAL ANALYSIS OF THE FREE-VIBRATION OF THICK RECTANGULAR-PLATES WITH DEPRESSIONS, GROOVES OR CUTOUTS

A solution is presented for the free vibration of very thick rectangul ar plates with depressions, grooves or cut-outs using three-dimensiona l elasticity equations in Cartesian coordinates. Simple algebraic poly nomials which satisfy the boundary conditions of the plate are used as trial functions in a Ritz approach. The plate is modelled as a parall elepiped, and the inclusions are treated quite straightforwardly by su btracting the contribution to the strain and kinetic energy expression s of the volume removed, before minimizing the functional. The approac h is demonstrated by considering a number of square thick plate cases, including a plate with a cylindrical groove, a shallow depression or a cylindrical cut-out.