Analyzing the free vibrations of a plate using finite difference and differential transformation method

摘要

This paper analyses the free vibrations of clamped and simply supported rectangular thin plates. A hybrid method which combines the finite difference method and the differential transformation method is employed to reduce the partial differential equations of the plate to a set of algebraic equations. The investigative parameters include the order of the differential transformation, the number of sub-domain spaces, the variable conditions and the type of initial condition. The numerical simulation results indicate that the solution of the natural frequency is more accurate when calculated using a higher number of sub-domains. The effect of the difference transformation order value (k) on the solution of the natural frequency is not significant when the combined T spectra method and differential transformation method is applied. The initial mode shape of the plate has a significant influence on the solution of the natural frequency. The current modeling results confirm the viability of using the hybrid method proposed in this paper to solve the free vibrations and natural frequency of clamped and simply supported plates.