Roles of domain decomposition method in plate vibrations : Treatment of mixed discontinuous periphery boundaries

The detailed development of a domain decomposition method (DDM) for the vibrational modelling of rectangular plates with mixed-edge boundary conditions is presented. In the DDM, the complex plate domain is decomposed into small simple subdomains and the appropriate shape function of each subdomain is represented by sets of admissible orthogonal polynomials generated using the Gram-Schmidt recurrence process. The continuity matrices that couple the eigenvectors of adjacent subdomains are derived based on the satisfaction of continuity conditions along the interconnecting boundaries. The stiffness and mass matrices of each subdomain after pre- and post-multiplication by the respective continuity matrices are assembled to form the global stiffness and mass matrices. To demonstrate the effectiveness and accuracy of the DDM, a vibration study of several partially mixed edge plates has been carried out. Convergence tests for example problems are presented in which the accuracy of the results is established. The frequency parameters and mode shapes obtained, where possible, are verified by comparison with data published in the open literature. © 1993.