Rayleigh-Ritz Method For Free Vibration of Mindlin Trapezoidal Plates

In the present paper, the free vibration of moderately thick trapezoidal plates has been studied. The analysis is based on the Mindlin shear deformation theory. The solutions are determined using the pb-2 Rayleigh-Ritz method. The transverse displacement and the rotations of the plate are approximated by Ritz functions defined as two dimensional polynomials of the trapezoidal domain variables and a basic function that satisfied as essential boundary conditions. Three different arrangements of boundary conditions are considered which are the cantilevered, the simply supported and the clamped edge conditions. The effects of both, transverse shear and rotary inertia are accounted. Convergence of the solutions is verified by considering polynomials of several subsequent degrees till the results converge. The present results are compared with those available in the open literature which indicates good agreement between the present results and those previously published. A set of tabulated results for a wide range of variation of both thickness to root width (H/a) and the trapezoid angle  for each of the three different cases of boundary conditions are presented.