On the Use of the Substructure Method for Vibration Analysis of Rectangular Plates with Discontinuous Boundary Conditions

A substructure method is presented for analysis of the free vibration of a rectangular plate with mixed edge boundary conditions. The method involves the partitioning of the entire plate domain into appropriate elements to approximate the deflection function of each element by a set of admissible orthogonal polynomials. The continuity conditions along the interconnecting boundaries provide the coupling between the coefficients of each element. Summing the strain and kinetic energies of each element, and minimizing the resulting Rayleigh quotient with respect to the unknown coefficients, leads to the governing eigenvalue equation for the entire plate. Several plate problems are solved to demonstrate the applicability and accuracy of the present method. Where possible, the results obtained are verified by comparisons with existing published values from the literature.