Transverse Vibration of Trapezoidal Plates of Variable Thickness: Symmetric Trapezoids

Abstract

A set of simple two-dimensional polynomial functions is employed as the admissible displacement function in the Rayleigh-Ritz energy approach for the free transverse vibration analysis of symmetric trapezoidal plates with linearly varying thickness. The admissible function consists the product of (i) a two-dimensional polynomial function and (ii) a basic function. The basic function is defined by the product of the equations of the prescribed continuous piecewise boundary shape each raised to the power of 0, 1 or 2, corresponding to a free, simply supported, or clamped edge, respectively. The set of functions generated ensures the satisfaction of all the kinematic boundary conditions at the outset. The proposed method is applied to solve several symmetric trapezoidal plates with different combinations of boundary conditions and variable thickness. The results, for some cases, are compared with the available published values from the open literature. These new results may serve as benchmark data for the development of other numerical methods.