带质量块微型双稳态压电板的动力学分析

DYNAMIC ANALYSIS OF MICRO BISTABLE PIEZOELECTRIC PLATE WITH PROOF MASS

本文对带质量块的微型双稳态压电板进行动力学分析.以中心固支四边自由的带质量块微型压电层合板为研究对象,应用应变梯度理论考虑尺寸效应,综合考虑力、电、热耦合作用,采用Von Karman大变形理论,运用Hamilton原理建立非线性动力学方程.利用特征值法探究不同内禀长度和不同压电铺设面积的情况下,温度和电压对其固有频率和稳定性的影响.其次研究了不同外激励下系统的非线性动力学响应.通过本文的研究发现,随着压电铺设面积的增大,力、电、热耦合效应增强,对系统的稳定性影响越显著;通过研究温度和电压对系统振动幅值的影响为振动控制提供了理论依据.同时发现尺寸效应对结构刚度影响较大,验证了微型结构考虑尺度效应的必要性.本文的研究结果会为今后的工程实际应用提供一定的理论参考价值.

In this paper, the dynamics analysis of Micro bistable piezoelectric plate with proof mass is carried out, where the plate center is fixed but the quadrilateral is free. The scale effect is considered by using the strain gradient theory. Considering the coupling effect of force, electric and thermal, the nonlinear dynamic equation is established with the aid of the Von Karman large deformation theory and the Hamilton principle. Firstly, by means of the eigenvalue method, the effect of temperature and voltage on its natural frequency and stability is ex- plored under the condition of different internal length scale parameters and different piezoelectric layer area. Mo- reover, the nonlinear dynamic response of the system under different external excitation is studied. It is found that with the increase of the piezoelectric area, the more obvious coupling effect of force, electricity and heat, the in- fluence on the system stability is increased significantly. Temperature and voltage can stimulate or restrain the vi- bration amplitude, which provides a theoretical basis for vibration control. Meanwhile, it is shown that the size effect has a great influence on the structural stiffness, which proves the necessity to considere the scale effect for the micro structure.