基于传统板理论的智能圆形FGM薄板自由振动研究

An Analytical Study on the Free Vibration of Smart Circular Thin FGM Plate Based on Classical Plate Theory

基于传统板理论(CPT)对圆形功能梯度(FG)薄板的自由振动性能进行分析。这种板具有2个由压电(PZT4)材料构成的均布驱动器。对FG底层板的材料特性进行假定,考虑了材料体积分数的能量分布,将材料沿厚度方向进行分级,并采用二次方程模拟沿压电覆层厚度方向分布的电势场。采用运动微分方程来模拟板的固定端边界条件。介绍了详细的数学推导过程,并采用数值分析来研究FG板的梯度变化对结构自由振动的影响。其分析结果得到了三维有限元分析结果的证实。

Analytical investigation of the free vibration behavior of thin circular functionally graded （FG） plates integrated with two uniformly distributed actuator layers made of piezoelectric （PZT4） material based on the classical plate theory （CPT） is presented in this paper. The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The differential equations of motion are solved analytically for clamped edge boundary condition of the plate, The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. The results are verified by those obtained from three-dimensional finite element analyses.