Based on the dynamic equilibrium differential equations including the effect of initial loads for plates, the dynamic finite element method (FEM) for analyzing the effect of initial loads on arbitrary shape plates was presented using parametric coordinate transformation method. To verify the method, the approximate solutions of fundamental frequency including the effect of initial loads for the clamped square plate, the simply supported equilateral triangle plate, the clamped ellipse plate, the clamped circular plate and the simply supported circular plate were derived by using the Galerkin method. The approximate solutions of first three frequencies including the effect of initial loads for the simply supported square plate were solved using the Rayleigh method. The frequencies obtained by the FEM are good agreement with those approximate solutions, the reliability and efficiency of the presented FEM and those approximate solutions were verified. The effect of initial loads on dynamic characteristic of arbitrary plates was analyzed by the presented FEM, useful conclusion are obtained. The effect of initial loads improves the bending stiffness of plate and enhances the frequencies of plates. The key physical factors governing the effect of initial loads on plates are the initial load, the ration of span to thickness and boundary condition etc. This effect of initial loads is not negligible, especial in thinner plates or plates with smaller stiffness, more attention should be turn to the effect of initial load in the calculation and analysis for plates.
ZHOU Shi-jun LIU De-gui .
Finite element analysis for effect of initial load on dynamic characteristic of arbitrary plates[J]. Journal of Vibration and Shock, 2014, 33(12): 15-23
PDF(2040 KB)
