A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation (Q5939394)

The paper examines vibration characteristics of thin isotropic elastic plates with cross-sectional discontinuities due to an abrupt change in thickness. The authors present an efficient and accurate semi-analytical method based on Rayleigh-Ritz procedure and domain decomposition method. The complex plate configurations are decomposed into appropriate subdomains, and orthogonally generated admissible polynomials are used as displacement functions. The author compute continuity matrices from compatibility conditions at interconnecting edges in order to couple the eigenvectors of adjacent subdomains. The global energy functional is constructed from individual stiffness and mass matrices of subdomains as in the finite element method. The basic problem examines a square domain, and it is assumed that the Kirchhoff-Love plate theory can be used. The authors consider three types of boundary conditions: simply supported, clamped-simply supported-clamped-simply supported, and fully clamped edges. The computed natural frequencies are given in tabular form, and the contours of some mode shapes are presented.