中文摘要：

为对变截面压电悬臂梁系统的性能进行预测、分析和优化,该文对部分覆盖压电材料的悬臂梁数学进行了建模和分析。首先根据系统的动能、悬臂梁和压电片的热力学焓等能量关系的描述,应用拉格朗日方程得到系统的机电运动方程;再采用假设模态法并依据压电悬臂梁的边界条件和相容条件,给出系统的模态振型和自然频率的计算方法。实验结果表明,测量得到的一、二阶模态频率与理论模型计算的误差小于1%,测得的频率响应和理论预测吻合,提高了压电悬臂梁模型预测的精度。

英文摘要：

Dynamic modeling and anaylzing of partly piezoelectric cantilever system is studied in order to predict, analyze and optimize the performance of discontinuous piezoelectric cantilever system. Firstly, the piezoelectric cantilever is segmented to prensent energy functions, which is substituted into the Lagrange equations to obtain electromechanical motion equation. Secondly, based on boundary conditions and compatibility conditions , calculations method of modal shape and natural frequency is given. Finally, experimental results illustrate that the error of measured frequency of the first and second modal and theoretical model calculations is less than 1%, improving the prediction accuracy of the piezoelectric cantilever system.