Solutions of Symmetries for Piezoelectric Stack Actuators

XIE Yu; FU Jing-li; CHEN Ben-yong

doi:10.21656/1000-0887.370048

Volume 37 Issue 8

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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. 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. doi: 10.21656/1000-0887.370048

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Solutions of Symmetries for Piezoelectric Stack Actuators

doi: 10.21656/1000-0887.370048

¹School of Mechanical Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China;²School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China（11272287；11472247；11372169）

Received Date: 2016-02-13
Rev Recd Date: 2016-03-01
Publish Date: 2016-08-15

Abstract

Abstract

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.
- piezoelectric stack,
- actuator,
- symmetry,
- conserved quantity

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References(27)

References

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