Abstract
This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness. The nonlinear equations of plates with variable thickness are extended to the dynamic case. The resulting equations can be solved by using an iterative method, a Galerkin’s approach and a perturbation method. Detailed solutions and numerical results are given for two kinds of boundary conditions, the clamped edge and the supported edge. The results show that the solutions for the case of the plates with uniform thickness can be included in the solution herin as a special case. The effect of various thickness parameters is investigated in detail. Also, a Runge-Kutta method is used to solve the free and forced vibrations of plates with variable thickness, and the results are obtained firstly. It has shown that the adoption of variable thickness plate would be useful in engineering design.
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