中文摘要：

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.

英文摘要：

The symmetries of piezoelectric stack actuators were investigated,and the solutions of conserved quantities and symmetries were given.The piezoelectric stack actuator of axial movement was considered and its structural characteristics were analyzed,accordingly the displacement and the flux linkage were selected as the generalized coordinates,then the electromechanical coupling Lagrangian equations were established with the energy method.Through the infinitesimal transformation of the displacement and flux linkage coordinates,the Noether symmetries and Lie symmetries were studied respectively,in turn the generalized Noether identity,the generalized Killing equations,the generalized Noether theorm and the Lie theorm were presented.The generators of the Noether symmetries and the Lie symmetries for the piezoelectric stack actuator were calculated,and the corresponding conserved quantities were derived.At last,with the obtained conserved quantities the solutions of symmetries were got,and the dynamic response curves of the actuator＇s displacement and speed were calculated under the changing control voltage.