多孔压电驻极体有效压电系数随时间演化行为的渐近均匀化研究  

Asymptotic Homogenization Method in Time-Dependent Effective Piezoelectric Coefficient of Cellular Piezoelectric Film

作　　者：余海冰[1] 万永平[1] 范亮亮[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2013年第4期517-524,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11072279)

摘　　要：由于聚合物的粘弹性,多孔压电驻极体厚度方向的有效压电系数d_(33)表现出随时间演化的行为.将多孔压电驻极体材料看成粘弹性聚合物形成的周期压电复合材料.基于弹性一粘弹性"对应原理",在Laplace域内建立多孔压电驻极体有效性质的渐近均匀化列式,基于代表性体元的有限元分析结果,获得Laplace域内有效压电系数d_(33)的离散值.对离散值最小二乘拟合,将拟合函数逆变换,得到时域内的多孔压电驻极体有效压电系数随时间的变化函数.通过几个算例,验证应用本方法分析多孔压电驻极体有效压电系数随时间演化行为的可行性.Due to the inherent viscosity of polymer, the effective piezoelectric coefficient d33 in the thickness direction of cellular piezoelectric film is time-dependent. The cellular piezoelectric film was viewed as the periodic piezoelectric composite with viscoelastic polymer. Based on the correspondence principle between elasticity and viscoelasticity, asymptotic homogenization was developed in Laplace transformed domain to find the effective properties of cellular piezoelectric film. Finite element analysis of the representative volume element was used to numerically obtain the effective piezoelectric coefficient d33. By means of the least square fitting and the subsequent inverse Laplace transform of the fitting function, the time-dependent effective piezoelectric coefficient in time domain was obtained. Several numerical examples were given to verify the present approach.

关 键 词：多孔压电驻极体 有效压电系数 渐近均匀化 粘弹性 LAPLACE变换 

分 类 号：O345[理学—固体力学]