Vibration of mindlin plates using boundary characteristic orthogonal polynomials

The vibration analysis of shear deformable plates formulated on the basis of first order Mindlin theory is presented. The displacement and rotational functions of the plates are approximated by sets of boundary characteristic orthogonal polynomials. The ease of generation and manipulation of these polynomial functions greatly enhances the computational efficiency of the numerical method. The energy functional of the shear deformable plates derived from the Mindlin plate theory is minimized in the Ritz procedure to arrive at the governing eigenvalue equation. Corresponding natural frequencies and mode shapes can be obtained by solving the eigenvalue equation. Computed frequency results for various boundary conditions, aspect ratiosa/band thickness ratiost/bare presented to demonstrate the effects of each factor on the vibration frequencies of moderately thick plates. Vibration mode shapes in the form of contour plots are presented for a thickness ratio oft/b= 0.1. These plots are believed to be the first known in the open literature. © 1995 Academic Press. All rights reserved.