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压电堆叠作动器的对称性求解

谢煜 傅景礼 陈本永

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. doi: 10.21656/1000-0887.370048
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. doi: 10.21656/1000-0887.370048
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

压电堆叠作动器的对称性求解

doi: 10.21656/1000-0887.370048
基金项目: 国家自然科学基金(11272287;11472247;11372169);长江学者和创新团队发展计划(IRT13097);浙江省重点科技创新团队项目(2013TD18)
详细信息
    作者简介:

    谢煜(1974—), 男, 副教授, 博士生(E-mail: xieyu1682003@163.com);傅景礼(1955—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: sqfujingli@163.com);陈本永(1965—), 男, 教授, 博士, 博士生导师(E-mail: chenby@zstu.edu.cn).

  • 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.
  • [1] Chopra I, Sirohi J.Smart Structures Theory [M]. New York: Cambridge University Press, 2014.
    [2] Kapuria S, Agrahari J K. Two dimensional shear lag solution for stress transfer between rectangular piezoelectric wafer transducer and orthotropic host plate[J].European Journal of Mechanics—A/Solids,2016,55: 181-191.
    [3] ZHAO Chun-sheng.Ultrasonic Motors Technologies and Application [M]. Beijing: Science Press, 2011.
    [4] HE Si-yuan, Chiarot P R, Park S. A single vibration mode tubular piezoelectric ultrasonic motor[J].IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,2011,58(5): 1049-1061.
    [5] LIU Ying-xiang, CHEN Wei-shan, YANG Xiao-hui, LIU Jun-kao. A T-shape linear piezoelectric motor with single foot[J].Ultrasonics,2015,56: 551-556.
    [6] Royston T J, Houston B H. Modeling and measurement of nonlinear dynamic behavior in piezoelectric ceramics with application to 1-3 composites[J].The Journal of the Acoustical Society of America,1998,104(5): 2814-2827.
    [7] Elka E, Elata D, Abramovich H. The electromechanical response of multilayered piezoelectric structures[J].Journal of Microelectromechanical Systems,2004,13(2): 332-341.
    [8] Low T S, Guo W. Modeling of a three-layer piezoelectric bimorph beam with hysteresis[J].Journal of Microelectromechanical Systems,1995,4(4): 230-237.
    [9] Weinberg M S. Working equations for piezoelectric actuators and sensors[J].Journal of Microelectromechanical Systems,1999,8(4): 529-533.
    [10] deVoe D L, Pisano A P. Modeling and optimal design of piezoelectric cantilever microactuators[J].Journal of Microelectromechanical Systems,1997,6(3): 266-270.
    [11] C?té F, Masson P, Mrad N, Cotoni V. Dynamic and static modelling of piezoelectric composite structures using a thermal analogy with MSC/NASTRAN[J].Composite Structures,2004,65(3/4): 471-484.
    [12] DONG Xing-jian, MENG Guang. Dynamic analysis of structures with piezoelectric actuators based on thermal analogy method[J].International Journal of Advanced Manufacturing Technology,2006,27(9): 841-844.
    [13] Hagood IV N W, McFarland A J. Modeling of a piezoelectric rotary ultrasonic motor[J].IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,1995,42(2): 210-224.
    [14] Adriaens H J M T S, de Koning W L, Banning R. Modeling piezoelectric actuators[J].IEEE/ASME Transactions on Mechatronics,2000,5(4): 331-341.
    [15] Elka E, Elata D, Abramovich H. The electromechanical response of multilayered piezoelectric structures[J].Journal of Microelectromechanical Systems,2004,13(2): 332-341.
    [16] 梅凤翔. 李群和李代数对约束力学系统的应用[M]. 北京: 科学出版社, 1999.(MEI Feng-xiang.Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems[M]. Beijing: Science Press, 1999.(in Chinese))
    [17] 秦孟兆, 王雨顺. 偏微分方程中的保结构算法[M]. 杭州: 浙江科学技术出版社, 2012.(QIN Meng-zhao, WANG Yu-shun.Structure-Preserving Algorithm for Partial Differential Equation[M]. Hangzhou: Zhejiang Science and Technology Publishing House, 2012.(in Chinese))
    [18] Martins N, Torres D F M. Noether’s symmetry theorem for nabla problems of the calculus of variations[J].Applied Mathematics Letters,2010,23(12): 1432-1438.
    [19] FU Jing-li, CHEN Li-qun. On Noether symmetries and form invariance of mechanico-electrical systems[J].Physics Letters A,2004,331(3/4): 138-152.
    [20] FU Jing-li, CHEN Li-qun, CHEN Ben-yong. Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices[J].Science China: Physics, Mechanics & Astronomy,2010,53(3): 545-554.
    [21] Feng M, Fredlund D G. Hysteretic influence associated with thermal conductivity sensor measurements[C]//Proceedings of the 52nd Canada Geotechnical Conference and Unsaturated Soil Group from Theory to the Practice of Unsaturated Soil Mechanics. Regina, Saskatchewan, Canada:[s. n.], 1999:651-657.
    [22] LONG Zi-xuan, ZHANG Yi. Noether’s theorem for fractional variational problem from El-Nabulsi extended exponentially fractional integral in phase space[J].Acta Mechanica,2014,225(1): 77-90.
    [23] 翟晓洋, 傅景礼. 汽车车体振动系统的对称性与守恒量研究[J]. 应用数学和力学, 2015,36(12): 1285-1293.(ZHAI Xiao-yang, FU Jing-li. Study on symmetries and conserved quantities of cehicle body vibration systems[J].Applied Mathematics and Mechanics,2015,36(12): 1285-1293.(in Chinese))
    [24] 杨绍普, 陈立群, 李韶华. 车辆-道路耦合系统动力学研究[M]. 北京: 科学出版社, 2012.(YANG Shao-pu, CHEN Li-qun, LI Shao-hua.Dynamics of Vehicle-Road Coupled System [M]. Beijing: Science Press, 2012.(in Chinese))
    [25] Yang S P, Li S H, Lu Y J. Investigation on dynamical interaction between a heavy vehicle and road pavement[J].Vehicle System Dynamics,2010,48(8): 923-944.
    [26] Mei F X, Wu H B.Dynamics of Constrained Mechanical Systems [M]. Beijing: Beijing Institute of Technology Press, 2009.
    [27] 毛剑琴, 李琳, 张臻, 李超, 马艳华. 智能结构动力学与控制[M]. 北京: 科学出版社, 2013.(MAO Jian-qin, LI Lin, ZHANG Zhen, LI Chao, MA Yan-hua.Smart Structure Dynamics and Control [M]. Beijing: Science Press, 2013.(in Chinese))
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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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