A GLOBAL APPROACH FOR VIBRATION OF THICK TRAPEZOIDAL PLATES

A global pb-2 Rayleigh-Ritz method is used to study the free vibration behaviour of trapezoidal Mindlin plates with different combinations of boundary conditions. The Mindlin theory is used to account for the effects of shear deformation and rotary inertia. The governing energy functional for the plate is derived and minimized to arrive at the eigenvalue equation. In the process, the shape functions are assumed in a set of two-dimensional mathematically complete polynomials which satisfy the geometric boundary conditions of the plate. This procedure has been implemented numerically to compute the vibration frequencies for trapezoidal Mindlin plates. Convergence and comparison studies have been carried out to verify the accuracy of this method. Sets of first known results have been presented for trapezoidal Mindlin plates of varying thickness, aspect ratio and boundary constraint. These new results enhance the database of vibration solutions.