梯度压电悬臂梁的解析解及其逆问题

Analytical Solutions and Inverse Problem of Functionally Gradient Piezoelectric Cantilever

在平面应变状态下,考虑材料压电参数的梯度特性,采用逆解法求解了悬臂梁受力偶和外加电压作用时的解析解,并通过与基于BaTiO3陶瓷所得实验值的对比发现,其结果与N层压电板组成的悬臂梁当N趋于∞时其端部弯曲位移值十分接近,且悬臂梁内部应力场逐渐减少为零的结论在此得到了验证.基于所得到的解析解,提出了梯度相物性参数识别的方法.

Based on the theory of elasticity, the bending behavior of piezoelectric cantilever with gradient property for piezoelectric parameter g31 is studied. By use of Airy stress function method, the solution of cantilever subjected to a couple and an electric field is obtained. The results obtained in present paper are compared with that from both experiment and other analytical models based on c_ceramics. It is found that the tip deflection of cantilever obtained in present paper agrees well with the result of N_morph cantilever when the number N gets to ∞. Present paper also gives a theoretical demonstration that all the mechanical stresses will be vanishing in FGM actuators. Additionally addressed in present paper is a method of parameter identification.