Three Dimensional Exact Solution for Free Vibration of Functionally Gradient Piezoelectric Circular Plate
Three Dimensional Exact Solution for Free Vibration of Functionally Gradient Piezoelectric Circular Plate
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发表时间：
2005
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通讯作者：
Zhongming Zheng
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作者：
Zhongming Zheng
对广义刚性滑动支承和广义弹性简支的功能梯度压电材料圆板的自由振动进行了精确的三维分析。根据轴对称传递各向同性压电材料的基本方程，采用有限汉克尔变换的方法建立了功能梯度压电圆板的状态空间方程。假设材料的力学和电学性能随厚度坐标的变化具有相同的指数规律，得到了广义刚性滑动支承和广义弹性简支圆板自由振动的精确三维频率方程。这个方程是一个超越方程。通过对该超越函数的求解，可以得到不同厚度和不同梯度变化的圆板的自由振动频率值。结果表明：频率随板材厚度的增加而增加，相同厚度的板材，频率随材料性能梯度的增加而减小。
An exact three dimensional analysis was presented for the free vibration of a functionally gradient piezoelectric material circular plate that is generalized rigid slipping supported and generalized elastic simply supported. According to the basic equations of axisymmetric transfer isotropic piezoelectric materials, the state space equations of the functionally gradient piezoelectric circular plate were developed by the method of finite Hankel transformation. Assuming that the mechanical and electric properties of the materials have the same exponential law dependence on the thickness-coordinate, an exact three dimensional frequency equations of the free vibration for generalized rigid slipping supported and generalized elastic simply supported circular plate was obtained. This equation is a transcendental equation. And the frequency values of free vibration for the circular plate with different thickness and different graded variation can be obtained by the solution of this transcendental function. The conclusion is that the frequency increases with the increasing thickness of plate, and the decreased frequency will be got with the increase of the material properties grads for the plate with the same thickness.