Method of domain decomposition in vibrations of mixed edge anisotropic plates

Abstract

This paper presents the first known study on the flexural vibration of anisotropic plates with mixed discontinuous periphery boundaries. A newly developed domain decomposition method is used in the analysis to derive the governing eigenvalue equation. In the solution process, the complex plate domain is decomposed into appropriate subdomains. The displacement functions of each subdomain are represented by sets of orthogonally generated polynomials that satisfy the essential geometric boundary conditions. From the compatibility requirements at the interconnecting boundaries, sets of continuity matrices are computed. These matrices are used to couple the respective eigenvectors of the adjacent subdomains. The stiffness and mass matrices of each subdomain after being pre- and post-multiplied by the corresponding continuity matrix, are assembled to form the global stiffness and mass matrices of the anisotropic plate. Convergence and comparison studies have been carried out on selected cases to establish the rate of convergence and degree of accuracy of the present formulation. A comprehensive range of frequency parameters and deflection mode shapes of anisotropic plates with different mixed edge configurations are obtained using the proposed method. The effects of fiber orientation and the partial mixed ratio on the vibrational response of these plates have been investigated in detail.