端部受弯矩作用的压电弹性层合梁的二维解析解

Two-Dimensional Analytic Solution to the Laminated Piezoelectric Beam Subjected to the Moments on Both Ends

利用压电弹性介质的二维本构关系 ,分别假定压电层和弹性层的应力分布 ,进而求得各自的位移分布 ,再通过层间连续条件和放松边界条件 ,推导出两端简支或一端固支的带压电层的弹性梁在端部受弯矩作用时的位移、电势分布的解析表达式 .最后以一端固支的层合梁为例 ,并与压电有限元的计算结果进行了比较 。

On the basis of two- dimensional constitutive relationships of piezoelectric materials,the stresses of piezoelectric layer and elastic layer were assumed respectively.The displacements of these two layers were obtained.Via the interface continuum conditions and the loosened boundaries,this paper derived an analytic solution to the simply supported laminated piezoelectric beam or cantilever beam subjected to the moments on both ends.A laminated cantiever beam was demonstrated for an example,and its results were compared with the results of FEM.Itis helpful to further research for the mechanism of distribution sens- ing of piezoelectric materials and the validation of numerical methods such as FEM.