## 留言板

 引用本文: 谢煜, 傅景礼, 陈本永. 压电堆叠作动器的对称性求解[J]. 应用数学和力学, 2016, 37(8): 778-790.
XIE Yu, FU Jing-li, CHEN Ben-yong. Solutions of Symmetries for Piezoelectric Stack Actuators[J]. Applied Mathematics and Mechanics, 2016, 37(8): 778-790. doi: 10.21656/1000-0887.370048
 Citation: XIE Yu, FU Jing-li, CHEN Ben-yong. Solutions of Symmetries for Piezoelectric Stack Actuators[J]. Applied Mathematics and Mechanics, 2016, 37(8): 778-790.

• 中图分类号: TB381

## Solutions of Symmetries for Piezoelectric Stack Actuators

Funds: The National Natural Science Foundation of China（11272287；11472247；11372169）
• 摘要: 研究了压电堆叠作动器的对称性，并给出了系统存在的守恒量和对称性解.以轴向运动的压电堆叠作动器为研究对象，根据其结构特点，选取位移和磁链作为广义坐标，运用能量方法，建立了压电堆叠作动器的Lagrange(拉格朗日)方程.引入位移和磁链广义坐标的无限小群变换，分别研究了压电堆叠作动器的Noether对称性和Lie对称性，给出了广义Noether恒等式、广义Killing方程、广义Noether定理和Lie定理，计算了压电堆叠作动器存在的Noether对称性和Lie对称性的生成元，并给出了相应系统存在的守恒量.最后，利用得到的守恒量，给出了压电堆叠作动器对称性解，并计算了在控制电压变化的情况下位移和速度的动态响应曲线.
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##### 出版历程
• 收稿日期:  2016-02-13
• 修回日期:  2016-03-01
• 刊出日期:  2016-08-15

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