结合薄膜变形原理和压电本构方程，在电压激励条件下，对弹性压电薄膜驱动器进行受力分析，建立压电驱动器横向位移计算模型。在文献提供的几何参数和材料物理参数的基础上，对比理论，文献试验以及模拟仿真的结果，偏差不超过10%，验证理论模型可行。并通过试验测试，进一步分析模型计算结果的准确性，结果表明理论计算与试验数据最大误差在7%以内。基于建立的数学模型，分析不同电压、不同半径比以及不同压电厚度和弹性膜厚度对圆形压电驱动器横向位移的影响。结果表明：圆形压电驱动器中心的横向位移随电压线性变化；在压电驱动器厚度和材料物理参数一定时，压电层与弹性层半径比为0.75时，压电驱动器中心横向位移最大；当电压、材料物理参数以及压电驱动器半径比固定的条件下，分析压电厚度和弹性膜厚度对圆形压电驱动器横向位移影响机理，在压电驱动器总厚度一定条件下，得到最优的压电厚度占总厚度的比值。通过分析不同几何参数对压电驱动器横向位移的影响，指导和优化压电驱动器的结构设计。
With the theory of thin diaphragm deformation and the piezoelectric constitutive equation, under the constant voltage conditions, an analytical model on deflection of a circular piezoelectric actuator is proposed to investigate the stress distribution of the actuator. Based on the geometric parameters and material properties of the literatures, the model results agree with the literature experimental data and simulations within 10%. Furthermore, the accuracy of model results is also validated by experiments with the maximal offset less than 7%. Thus, the model results are used for studying the impacts on piezoelectric actuator displacement in the different parameters, which include the voltage, the radius ratio and the thickness of piezoelectric layer and elastic layer. The results show that:the displacement of circular piezoelectric actuator linearly varies with the voltage, and the optimized radius ratio of piezoelectric layer and elastic layer is 0.75 to obtain the maximal center displacement of circular piezoelectric actuator. Moreover, when the voltage, material properties and radius ratio are fixed, the impacts on the displacement of circular piezoelectric diaphragm under the different thickness of piezoelectric layer and elastic layer are analyzed. With the fixed thickness of the multi-layer, the optimal thickness ratio of piezoelectric layer and elastic layer is obtained by analytical model results. By analyzing the different influences of these parameters, the structure design of a circular piezoelectric actuator is guided and optimized.
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