压电结构系统机电耦合的强化与多阶共振抑制
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摘要
提高压电系统的机电耦合程度可以提高压电分支电路对于结构机械振动的抑制效果.提出了一种可同时提高压电系统多阶模态机电耦合程度、进而实现对系统多阶共振进行控制的方法.首先通过对压电悬臂梁模型的理论研究揭示了将压电片的电极离散、并以不同方式连接可以导致系统的机电耦合程度发生改变的现象.在此基础上导出可刻划此现象的模态机电耦合函数;提出通过对模态机电耦合函数的优化寻求压电片电极的最佳离散方式和最佳连接方式,以获得对应某一模态的最大机电耦合函数值.为了对多阶共振抑制,提出引入选通电路,通过对含有选通电路的模态机电耦合函数的参数优化实现同时提高压电系统多模态机电耦合程度、进而抑制多阶共振的方法.结合数值实例对此方法进行说明.
Enhancing the electromechanical coupling of a piezoelectric system is an effective way to suppress the vibration of the system by the piezoelectric shunt technique.A method was proposed which can increase the multiple-mode electromechanical coupling for a piezoelectric system.From the research of piezoelectric cantilever beam model,it was found that the electromechanical coupling depends on the position of the electrode on the piezoelectric materials,as well as the way to connect to the shunted circuits.The modal electromechanical coupling function was proposed to describe this phenomenon.For the sake to get one modal coupling maximum,the best position of the electrode and the best connection ways can be obtained through optimizing the modal electromechanical coupling function.The ‘current flowing'circuits was proposed to make multiple-mode electromechanical coupling enhancement possible and to realize multimode vibration suppression.This method was verified through numerical examples.
Enhancing the electromechanical coupling of a piezoelectric system is an effective way to suppress the vibration of the system by the piezoelectric shunt technique.A method was proposed which can increase the multiple-mode electromechanical coupling for a piezoelectric system.From the research of piezoelectric cantilever beam model,it was found that the electromechanical coupling depends on the position of the electrode on the piezoelectric materials,as well as the way to connect to the shunted circuits.The modal electromechanical coupling function was proposed to describe this phenomenon.For the sake to get one modal coupling maximum,the best position of the electrode and the best connection ways can be obtained through optimizing the modal electromechanical coupling function.The ‘current flowing'circuits was proposed to make multiple-mode electromechanical coupling enhancement possible and to realize multimode vibration suppression.This method was verified through numerical examples.
引文
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[5]王建军,李其汉.具有分支电路的可控压电阻尼减振技术[J].力学进展,2003,33(3):389-403Wang Jianjun,Li Qihan.Recent advances of vibration damping and control using piezoelectric materials with shunted circuits[J].Advances in Mechanics,2003,33(3):389-403(in Chinese)
[6]陈伟民,管德,李敏,等.压电驱动器用于薄板型结构振动主动控制研究[J].航空学报,2001,22(2):109-112Chen Weimin,Guan De,Li Min,et al.Active vibration control of thin plate with piezoelectric actuators[J].Acta Aeronautica et Astronautica Sinica,2001,22(2):109-112(in Chinese)
[7]Guyomar D,Richard C,Mohammadi S.Semi-passive random vibration control based on statistics[J].Journal of Sound and Vibration,2007,307(3-5):818-833
[8]Park C H,Inman D J.Enhanced piezoelectric shunt design[J].Shock and Vibration,2003,10(2):127-133
[9]De Marneffe B,Preumont A.Vibration damping with negative capacitance shunts:theory and experiment[J].Smart Materials and Structures,2008,17(3):35015
[10]Carlos N E,Kikuchi S.Design of piezoelectric transducers using topology optimization[J].Smart Materials and Structures,1999,8(3):350-364
[11]Belloli A,Ermanni P.Optimum placement of piezoelectric ceramic modules for vibration suppression of highly constrained structures[J].Smart Materials and Structures,2007,16(5):1662-1671
[12]Liao Y B,Sodano H A.Optimal placement of piezoelectric material on a cantilever beam for maximum piezoelectric damping and power harvesting efficiency[J].Smart Materials and Structures,2012,21(10):105014
[13]Vasques C M A.Improved passive shunt vibration control of smart piezo-elastic beams using modal piezoelectric transducers with shaped electrodes[J].Smart Materials and Structures,2012,21(12):125003
[14]Hollkamp J J.Multimodal passive vibration suppression with piezoelectric materials and resonant shunts[J].Journal of Intelligent Material Systems And Structures,1994,5(1):49-58
[15]Behrens S,Moheimani S O R.Current flowing multiple-mode piezoelectric shunt dampener[C]//Proceedings of SPIE-the International Society for Optical Engineering.Bellingham,WA:SPIE,2002,4697:217-226
[16]Erturk A,Inman D J.A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters[J].Journal of Vibration and Acoustics-Transactions of the ASME,2008,130(4):041002-1-15
[2]Crawley E F,de Luis J,Hagood N W,et al.Development of piezoelectric technology for applications in control of intelligent structures[M].Atlanta,GA:IEEE,1988
[3]Moheimani S O R.A survey of recent innovations in vibration damping and control using shunted piezoelectric[J].IEEE Transactions on Control Systems Technology,2003,11(4):482-499
[4]姚军,李岳锋.压电薄板的建模和阻尼的准独立模态控制[J].航空学报,2000,21(2):159-163Yao Jun,Li Yuefeng.Modeling of piezoelectric thin plates and quasi-independent modal control for damping[J].Acta Aeronautica et Astronautica Sinica,2000,21(2):159-163(in Chinese)
[5]王建军,李其汉.具有分支电路的可控压电阻尼减振技术[J].力学进展,2003,33(3):389-403Wang Jianjun,Li Qihan.Recent advances of vibration damping and control using piezoelectric materials with shunted circuits[J].Advances in Mechanics,2003,33(3):389-403(in Chinese)
[6]陈伟民,管德,李敏,等.压电驱动器用于薄板型结构振动主动控制研究[J].航空学报,2001,22(2):109-112Chen Weimin,Guan De,Li Min,et al.Active vibration control of thin plate with piezoelectric actuators[J].Acta Aeronautica et Astronautica Sinica,2001,22(2):109-112(in Chinese)
[7]Guyomar D,Richard C,Mohammadi S.Semi-passive random vibration control based on statistics[J].Journal of Sound and Vibration,2007,307(3-5):818-833
[8]Park C H,Inman D J.Enhanced piezoelectric shunt design[J].Shock and Vibration,2003,10(2):127-133
[9]De Marneffe B,Preumont A.Vibration damping with negative capacitance shunts:theory and experiment[J].Smart Materials and Structures,2008,17(3):35015
[10]Carlos N E,Kikuchi S.Design of piezoelectric transducers using topology optimization[J].Smart Materials and Structures,1999,8(3):350-364
[11]Belloli A,Ermanni P.Optimum placement of piezoelectric ceramic modules for vibration suppression of highly constrained structures[J].Smart Materials and Structures,2007,16(5):1662-1671
[12]Liao Y B,Sodano H A.Optimal placement of piezoelectric material on a cantilever beam for maximum piezoelectric damping and power harvesting efficiency[J].Smart Materials and Structures,2012,21(10):105014
[13]Vasques C M A.Improved passive shunt vibration control of smart piezo-elastic beams using modal piezoelectric transducers with shaped electrodes[J].Smart Materials and Structures,2012,21(12):125003
[14]Hollkamp J J.Multimodal passive vibration suppression with piezoelectric materials and resonant shunts[J].Journal of Intelligent Material Systems And Structures,1994,5(1):49-58
[15]Behrens S,Moheimani S O R.Current flowing multiple-mode piezoelectric shunt dampener[C]//Proceedings of SPIE-the International Society for Optical Engineering.Bellingham,WA:SPIE,2002,4697:217-226
[16]Erturk A,Inman D J.A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters[J].Journal of Vibration and Acoustics-Transactions of the ASME,2008,130(4):041002-1-15