A global continuum Ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in

The development of a continuum Ritz model for twisted plate vibration on the basis of minimization of the energy functional is presented. This method involves the use of a set of orthogonally generated pb-2 shape functions to approximate the transverse and in-plane deflections. In this paper, a two-dimensional recurrence formula is proposed to generate this set of functions. During the orthogonalization process, a basic function is introduced to each transverse and in-plane displacement to ensure the automatic satisfaction of the essential boundary conditions. The whole process can be easily implemented numerically and the accuracy of the method can be achieved by increasing the number of terms used in the polynomial functions. Following the above procedures, a governing eigenvalue equation is derived. This equation is solved to determine the vibration response of trapezoidal plates with initial twist. In order to verify the validity and reliability of this method, in addition to the convergence study, the present results are compared with the available values from the literature where possible. © 1994.