基于压电悬臂梁的驱动器与传感器性能分析的精确解析模型

三层压电梁结构在电场作用下发生变形后会产生诱发电势，进而改变材料整体电势分布，本文考虑此变形和电势耦合效应，基于欧拉-伯努利梁变形理论，推导出能够准确预测压电智能悬臂梁传感器与驱动器性能的解析表达式。考虑压电梁结构弯曲变形后产生的电场影响，建立了三层压电梁结构的控制方程；建立了压电梁作为驱动器时端部输出位移、驱动力矩与输入电压之间联系的解析表达式，以及作为传感器时输出电压与端部作用力之间联系的解析表达式。通过与ANSYS有限元模拟结果以及传统的驱动器和传感器性能表达式的对比，验证了所推导的解析表达式的准确性。

An accurate analytical expression for predicting the performance of piezoelectric cantilever based actuators and sensors

The deformation of the three-layered piezoelectric beam in the electric field will arise the induced potential, and then change the distribution of the whole structural electric potential. Considering the coupling effect of the deformation and potential, the accurate analytical expressions, based on the Euler-Bernoulli beam theory, for predicting the performance of three-layered piezoelectric cantilever actuators and sensors, were derived. In the derivation process, the governing equation of three-layered piezoelectric beam structure was established with considering the effect of the electric field induced by the structural bending deformation, and then two analytical expressions for piezoelectric actuators and sensors were obtained with two different boundary conditions. These two analytical expressions related tip output displacement with driving moment and input voltage for piezoelectric actuators, and input voltage with tip force for piezoelectric sensors, respectively. The accuracy of the present expressions was illustrated by comparison of results obtained from ANSYS finite element simulation and conventional expressions for test problems.