基于压电网络的四边固支板多阶共振抑制
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摘要
利用四边固支板横向自由振动的精确解作为模态坐标,在模态空间求解了四边固支压电网络板的机电耦合动力学方程.基于对压电网络板在模拟单点激励下谐响应行为的计算分析,得到了控制其各阶共振的压电网络电路元件最优电学参数.电感电阻并联型四边固支压电网络板与四边简支压电网络板不同,其具有多个局部最优电学参数.通过分析这些最优参数对其他阶共振的影响,发现四边固支压电网络板具有多阶共振抑制效果,与电阻相比,该效果对电感更加敏感.电感电阻并联型四边固支压电网络板可以实现比电阻型四边固支压电网络板更好的单模态振动抑制效果,但同时其多模态振动抑制效果会降低.
The exact solutions for transverse free vibrations of a clamped plate were adopted as the modal coordinates to solve the given electromechanical coupled kinetic equations of clamped piezo electro mechanicalplate in modal space. After the computational analysis was conducted for harmonic response of the clamped piezo electro mechanical-plate which was stimulated under single-point excitation force,the optimal parameters of electrical components in piezoelectric networks used to suppress different resonances were obtained. For the clamped piezo electro mechanical-plate with parallel resistors and inductors,it has more than one local optimal parameters comparing with a simply supported plate. The clamped piezo electro mechanical-plate has the ability to suppress multimode vibration by analyzing the effectiveness of these optimal parameters on other resonances. In addition,the effectiveness is more sensitive to inductance comparing with resistance. The clamped piezo electro mechanical-plate with parallel resistors and inductors is more effective than piezo electro mechanical-plate only with resistors in reducing resonant response at single resonant frequency,while the multiplemode vibration suppression effectiveness of it with parallel resistors and inductors will be decreased.
The exact solutions for transverse free vibrations of a clamped plate were adopted as the modal coordinates to solve the given electromechanical coupled kinetic equations of clamped piezo electro mechanicalplate in modal space. After the computational analysis was conducted for harmonic response of the clamped piezo electro mechanical-plate which was stimulated under single-point excitation force,the optimal parameters of electrical components in piezoelectric networks used to suppress different resonances were obtained. For the clamped piezo electro mechanical-plate with parallel resistors and inductors,it has more than one local optimal parameters comparing with a simply supported plate. The clamped piezo electro mechanical-plate has the ability to suppress multimode vibration by analyzing the effectiveness of these optimal parameters on other resonances. In addition,the effectiveness is more sensitive to inductance comparing with resistance. The clamped piezo electro mechanical-plate with parallel resistors and inductors is more effective than piezo electro mechanical-plate only with resistors in reducing resonant response at single resonant frequency,while the multiplemode vibration suppression effectiveness of it with parallel resistors and inductors will be decreased.
引文
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[11]Batra R C,Dell’Isola F,Vidoli S,et al.Multimode vibration suppression with passive two-terminal distributed network incorporating piezoceramic transducers[J].International Journal of Solids and Structures,2005,42(11-12):3115-3132.
[12]Dell’Isola F,Henneke E G,Porfiri M.Synthesis of electrical networks interconnecting PZT actuators to damp mechanical vibrations[J].International Journal of Applied Electromagnetics and Mechanics,2001,14(1-4):417-424.
[13]Vidoli S,Dell’Isola F.Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks[J].European Journal of Mechanics,A/Solids,2001,20(3):435-456.
[14]李琳,易凯军.压电网络板的机电耦合动力学特性[J].北京航空航天大学学报,2014,40(7):873-880.Li L,Yi K J.Electromechanical coupled dynamic characteristics of the plate with piezoelectric network[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(7):873-880(in Chinese).
[15]易凯军,李琳.压电网络板的振动控制原理与控制效果[J].北京航空航天大学学报,2014,40(11):1629-1636.Yi K J,Li L.Vibration-controlling principle and controlling effectiveness of piezo-electro-mechanical plate[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(11):1629-1636(in Chinese).
[16]Xing Y F,Liu B.New exact solutions for free vibrations of rectangular thin plates by symplectic dual method[J].Acta Mechanica Sinica,2009,25(2):265-270.
[2]Hagood N W,von Flotow A.Damping of structural vibrations with piezoelectric materials and passive electrical networks[J].Journal of Sound and Vibration,1991,146(2):243-268.
[3]Park C H,Inman D J.Enhanced piezoelectric shunt design[J].Shock and Vibration,2003,10(2):127-133.
[4]de Marneffe B,Preumont A.Vibration damping with negative capacitance shunts:Theory and experiment[J].Smart Materials and Structures,2008,17(3):035015.
[5]张付兴,阎绍泽.压电陶瓷片与多种电路机电耦合的阻尼特性[J].清华大学学报:自然科学版,2005,45(8):1040-1043.Zhang F X,Yan S Z.Damping characteristics of piezoceramics shunted by various types of electrical circuits[J].Journal of Tsinghua University:Science and Technology,2005,45(8):1040-1043(in Chinese).
[6]Hollkamp J J.Multimodal passive vibration suppression with piezoelectric materials and resonant shunts[J].Journal of Intelligent Material Systems and Structures,1994,5(1):49-57.
[7]Park C H,Park H C.Multiple-mode structural vibration control using negative capacitive shunt damping[J].Journal of Mechanical Science and Technology,2003,17(11):1650-1658.
[8]刘莹,卜雄洙,庞俊恒.基于压电分支阻尼的多模态电路被动控制的研究和应用[J].南京理工大学学报:自然科学版,2007,31(3):300-303.Liu Y,Bu X Z,Pang J H.Study and application of passive control of multiple mode based on piezoelectric shunt damping[J].Journal of Nanjing University of Science and Technology:Natural Science,2007,31(3):300-303(in Chinese).
[9]李琳,刘学.压电结构系统机电耦合的强化与多阶共振抑制[J].北京航空航天大学学报,2014,40(8):1011-1016.Li L,Liu X.Enhancement of electromechanical coupling for piezoelectric system and suppression of multimode vibration[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(8):1011-1016(in Chinese).
[10]Dell’Isola F,Porfiri M,Vidoli S.Piezoelectro mechanical(PEM)structures:Passive vibration control using distributed piezoelectric transducers[J].Comptes Rendus Mécanique,2003,331(1):69-76.
[11]Batra R C,Dell’Isola F,Vidoli S,et al.Multimode vibration suppression with passive two-terminal distributed network incorporating piezoceramic transducers[J].International Journal of Solids and Structures,2005,42(11-12):3115-3132.
[12]Dell’Isola F,Henneke E G,Porfiri M.Synthesis of electrical networks interconnecting PZT actuators to damp mechanical vibrations[J].International Journal of Applied Electromagnetics and Mechanics,2001,14(1-4):417-424.
[13]Vidoli S,Dell’Isola F.Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks[J].European Journal of Mechanics,A/Solids,2001,20(3):435-456.
[14]李琳,易凯军.压电网络板的机电耦合动力学特性[J].北京航空航天大学学报,2014,40(7):873-880.Li L,Yi K J.Electromechanical coupled dynamic characteristics of the plate with piezoelectric network[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(7):873-880(in Chinese).
[15]易凯军,李琳.压电网络板的振动控制原理与控制效果[J].北京航空航天大学学报,2014,40(11):1629-1636.Yi K J,Li L.Vibration-controlling principle and controlling effectiveness of piezo-electro-mechanical plate[J].Journal of Beijing University of Aeronautics and Astronautics,2014,40(11):1629-1636(in Chinese).
[16]Xing Y F,Liu B.New exact solutions for free vibrations of rectangular thin plates by symplectic dual method[J].Acta Mechanica Sinica,2009,25(2):265-270.