Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions.