Application of Maple V to the nonlinear vibration analysis of circular plate with variable thickness

This paper is concerned with the application of Maple V to the nonlinear vibration problems of circular plates with variable thickness. In this paper, the nonlinear equations of plates of variable thickness to the dynamic case can be solved by using the computer algebra systems method. Details of solution expressions and numerical results are given in computer algebra systems forms, for two kinds of boundary conditions, which are the clamped edge and the supported edge. The numerical results show that the solutions of the paper contain other cases when the plates are of uniform thickness. The effect of various thickness parameters has been investigated in detail. In addition, a Runge-Kutta method is used to solve the free vibration and the maximum deflection response to a uniformly distributed step load of plates with variable thickness. It is shown that the adoption of variable thickness plate would be useful in engineering design. (C) 1999 Elsevier Science Ltd. All rights reserved.