压电圆柱棒基于变分渐近法的广义Timoshenko模型

基于变分渐近方法,对外侧表面无规定电势作用的压电圆柱棒构建了一种新的广义Timoshenko模型,以准确捕捉介质效应、压电材料极化以及机-电耦合性质。利用细长比作为小参数渐近近似计算压电圆柱棒的三维机电焓,得到等效的一维机电焓,并将二阶渐近修正的能量项保存在近似机电焓表达式中。为便于工程应用,将近似机电焓转换为具有6个力自由度和1个附加电自由度的广义Timoshenko模型。通过截面极化下悬臂压电圆柱棒端部挠度算例表明：所构建的模型与ANSYS三维多物理场耦合模拟具有很好的一致性,并能以很小的精度损失极大地简化分析过程。

A NEW GENERALIZED TIMOSHENKO MODEL FOR PIEZOELECTRIC CYLINDRICAL RODS BY USING THE VARIATIONAL ASYMPTOTIC METHOD

Based on the Variational Asymptotic Method (VAM), a new generalized Timoshenko model is constructed for piezoelectric rods, of which no electric potential along lateral surfaces is specified. The model is to accurately capture the effects of the dielectric, the polarization of piezoelectric materials as well as the coupled electromechanical nature. The three-dimensional (3D) electromechanical enthalpy is asymptotically approximated by the VAM, using the ratio of the cross-sectional radius to the length of the rod as the small parameter. As a result, an equivalent one-dimensional electromechanical enthalpy is developed. In the meantime, the energy terms, which are asymptotically corrected up to the second order, are kept in the approximated enthalpy expression. For ease of practical application, the approximated enthalpy is then transformed into a generalized Timoshenko model which involves the traditional six mechanical degrees of freedom along with an additional electrical degree of freedom. The cross-sectional polarization example of a cantilever piezoelectric bar shows that results from the proposed model agree well with the ANSYS 3D multiphysical simulation, confirming the reliability of the model as well as its capability in simplifying the analysis with insignificant loss in accuracy.