压电驱动器非线性机电耦合动力学求解与验证

摘要/Abstract

摘要：

基于压电非线性效应和位移非线性效应建立了压电驱动器非线性机电耦合动力学方程,应用Linz Ted-Poincaré法对弱非线性自由振动、接近共振时受迫振动及亚谐波振动响应方程进行推导,比较了压电驱动器在非线性及线性条件下响应的区别,使用四阶Runge-Kutta数值法和实验对理论推导进行了验证。结果表明:在两种非线性效应中,压电非线性对压电驱动器振动响应的影响是主要的;非线性数值解与解析解吻合较好,实验频率更接近非线性共振频率。

关键词: 压电驱动器, 非线性的, 机电耦合动力学；Linz Ted- Poincaré, 法

Abstract:

On the basis of non-linear piezoelectric effect and non-linear displacement effect,the non-linear electromechanical-coupled dynamic equations of piezoelectric actuator were established.Applying Linz Ted-Poincaré method,response equations of weak nonlinear free vibration, force vibration near to natural frequency,subharmonic vibration were deduced.And the comparison between non-linear response and linear response was investigated. Using the fourth order Runge-Kutta and experimental method, the theoretical derivation was verified.Results show,in the two types of non-linear effects, the impact of piezoelectric non-linear effect on actuator is primary. Numerical results agree well with analytical solutions, and testing frequencies are close to non-linear resonance frequencies.

Key words: piezoelectric actuator;non-linear;electromechanical-coupled , dynamics;Linz , Ted-Poincaré, method

中图分类号:

TH113.1

李冲, 许立忠, 邢继春. 压电驱动器非线性机电耦合动力学求解与验证[J]. 中国机械工程, 2015, 26(24): 3275-3281.

Li Chong, Xu Lizhong, Xing Jichun. Solution and Validation of Non-linear Electromechanical-coupled Dynamics for Piezoelectric Actuator[J]. China Mechanical Engineering, 2015, 26(24): 3275-3281.

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http://www.cmemo.org.cn/CN/Y2015/V26/I24/3275

参考文献

[1]Liu Xiujuan,Zhou Kechao,Zhang Xiaoyong,et al.Development,Modeling and Application of Piezoelectric Fiber Composites[J]. Transactions of Nonferrous Metals Society of China(English Edition),2013,23(1):98-107.
[2]Dragan A,Bryan B,Shashank P.Millipede-inspired Locomotion through Novel U-Shaped Piezoelectric Motors[J].Smart Materials and Structures, 2014,23(3),037001.
[3]Toyama S.Spherical Ultrasonic Motor for Pipe Inspection Robot[J]. Applied Mechanics and Materials,2012,186:3-11.
[4]Tomoaki M.Micro Ultrasonic Motor Using a One Cubic Millimeter Stator[J]. Sensors and Actuators A:Physical,2014,213:102-107.
[5]沈大雷.南航助“嫦娥”完美登月[N].中国教育报,2013-12-18(8).
[6]Chen Weishan,Liu Yingxiang,Yang Xiaohui,et al.Ring-type Traveling Wave Ultrasonic Motor Using a Radial Bending Mode[J].IEEE Trans. Ultrason. Ferroelectr. Freq. Control,2014,61(1):197-202.
[7]Oliver B.Harmonic Piezodrive-miniaturized Servo Motor[J].Mechatronics,2000,10(4):545-554.
[8]Li Chong,Xing Jichun,Xu Lizhong.Coupled Vibration of Driving Sections for an Electromechanical Integrated Harmonic Piezodrive System[J].AIP Advances,2014,4(3):031320.
[9]Vahid H,Tegoeh T.Dynamic Modeling of 3-DOF Pyramidal-shapedpiezo-driven Mechanism[J].Mechanism and Machine Theory, 2013,70:225-245.
[10]王光庆.压电叠堆式发电装置的建模与仿真分析[J].中国机械工程,2009,20(19): 2298-2304.
Wang Qingguang.Modeling and Simulation of a Piezoelectric Stacked Generator[J].China Mechanical Engineering,2009,20(19):2298-2304.
[11]Shahrokh H-H,Iman N,Mahmood F,et al.Nonlinear Free Vibration of Piezoelectric Nanobeams Incorporating Surface Effects[J]. Smart Materials and Structures,2014,23(3):035012.
[12]Ebrahimi F,Rastgoo A.Nonlinear Vibration Analysis of Piezo-thermo-electrically Actuated Functionally Graded Circular Plates[J]. Archive of Applied Mechanics,2011,81(3):361-383.
[13]郭抗抗,曹树谦.考虑材料非线性时压电发电悬臂梁的主共振响应分析[J].振动与冲击,2014,33(19):8-16.
Guo Kangkang,Cao Shuqian.Primary Resonance of Cantilevered Piezoelectric Energy Harvesters Considering Nonlinearities of Piezoelectric Material[J].Journal of Vibration and Shock,2014,33(19):8-16.
[14]Tan Ping,Tong Liyong.A One-dimensional Model for Non-linear Behaviourof Piezoelectric Composite Materials[J].Composite Structures, 2002,58(4):551-561.

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