压电弹性梁主共振响应的时滞加速度反馈控制

PDF(1279 KB)

振动与冲击 ›› 2016, Vol. 35 ›› Issue (24) : 1-5.

论文

彭剑，张改，胡霞，谢献忠

作者信息 +

Time-delayed acceleration feedback control of primary resonance of piezoelectric elastic beams

PENG Jian, ZHANG Gai, HU Xia, XIE Xian-zhong

Author information +

文章历史 +

摘要

应用时滞加速度反馈控制方法研究压电弹性梁主共振响应的减振控制。基于Hamilton原理和时滞加速度闭环反馈控制策略，建立了压电耦合弹性梁的非线性动力学模型。采用多尺度方法，得到了受控梁主共振响应的一阶近似解及稳定性条件，进而给出了响应峰值和临界激励幅值的表达式，并给出算例分析。结果表明：采用时滞加速度反馈控制可以有效减振，其主共振响应受时滞值周期性影响，合理选取控制增益和时滞值，可以避免主共振区及多值不稳定解，提高振动控制效果。

Abstract

The time-delayed acceleration feedback control method is applied to study the primary resonance response of vibration control of piezoelectric flexible beam. Based on the Hamilton principle and a closed-loop feedback control strategy with delay acceleration, the piezoelectric coupling nonlinear dynamic model of the elastic beam are established. Utilizing the multiple scale method, the first-order approximate solution and the stability condition of the primary resonance response of controlled beam are obtained. And the peak amplitude and the critical excitation amplitude are given. It is shown that using time-delayed acceleration feedback control can effective vibration reduction, the primary resonance response is affected by the delay value periodically. Reasonable selection of control gain and time delay value can avoid the resonance region and multiple values are not stable solution, and improve the effect of vibration control.

导出引用

彭剑，张改，胡霞，谢献忠. 压电弹性梁主共振响应的时滞加速度反馈控制[J]. 振动与冲击, 2016, 35(24): 1-5

PENG Jian, ZHANG Gai, HU Xia, XIE Xian-zhong. Time-delayed acceleration feedback control of primary resonance of piezoelectric elastic beams[J]. Journal of Vibration and Shock, 2016, 35(24): 1-5

参考文献

[1] 欧进萍. 结构振动控制—主动、半主动和智能控制[M].北京：科学出版社，2003.
OU Jin-ping. Structural vibration control—active, semi-active and intelligent control [M]. Beijing: Science Press, 2003.
[2]Hiroshi Y, Shigenobu S, Nobuharu A. Stabilization of the parametric resonance of a cantilever beam by bifurcation control with a piezoelectric actuator[J]. Nonlinear Dynamics, 2001, 26(2): 143-161.
[3] 朱辰钟,叶敏. 参强联合作用非线性结构动力学实验建模[J]. 力学学报, 2013,45(1): 116-128.
ZHU Chen-zhong YE Min. Research of dynamic experimental modeling for nonlinear structure under parametric and forced excitation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013,45(1): 116-128.
[4]王在华，胡海岩. 时滞动力系统的稳定性与分岔：从理论走向应用[J]. 力学进展, 2013, 43(1):1-20.
WANG Zai-hua, Hu Hai-yan. Stability and bifurcation of delayed dynamics systems: From theory to application[J], 2013, 43(1):1-20.
[5]冯志宏, 霍睿. 压电耦合悬臂梁的时滞反馈控制及稳定性分析[J]. 振动与冲击, 2011, 30(6): 181-184.
FENG Zhi-hong, HUO Rui. Time-delay feedback control and stability analysis of piezoelectric-coupling cantilever beam[J]. Journal of Vibration and Shock, 2011, 30(6): 181-184.
[6]陈龙祥，蔡国平. 旋转运动柔性梁的时滞主动控制实验研究[J]. 力学学报, 2008, 40(10): 520-527.
CHEN Long-xiang, CAI Guo-ping. Experimental study on active control of a rotating flexible beam with time delay [J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(10): 520-527.
[7]赵艳影, 徐鉴. 时滞非线性动力吸振器的减振机理[J].力学学报, 2008,40(1):98-105.
ZHAO Yan-ying, XU Jian. Mechanism analysis of delayed nonlinear vibration absorber[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008,40(1):98-105.
[8]李欣业;张利娟;张华彪. 陀螺系统的受迫振动及其时滞反馈控制[J].振动与冲击 2012, 31(9): 63-68.
LI Xin-ye; ZHANG Li-juan; ZHANG Hua-biao. Forced Vibration of a Gyroscope System and Its Delayed Feedback Control[J]. Journal of vibration and shock, 2012, 31(9): 63-68.
[9]尚慧琳，李伟阳，韩元波. 一类相对转动系统的复杂运动及时滞速度反馈控制[J]. 振动与冲击, 2015, 34(12): 127-132.
SHANG Hui-lin LI Wei-yang HAN Yuan-bo. The complex dynamics of a relative rotation system and its control by delay velocity feedback. Journal of vibration and shock, 2015, 34(12): 127-132.
[10]Daqaq M F, Alhazza K A, Arafat H N. Non-linear vibrations of cantilever beams with feedback delays [J]. International Journal of Non-Linear Mechanics, 2008, 43: 962-978.
[11]Masoud Z, Daqaq M F, Nayfeh N H. Pendulation reduction of small telescopic cranes[J]. Journal of Vibration and Control, 2004, 10(8): 1167-1179.
[12]Masoud Z, Nayfeh A H, Al-Mousa A. Delayed-position feedback controller for the reduction of payload pendulations on rotary cranes [J]. Journal of Vibration and Control, 2003, 9(1-2): 257-277.
[13]孙清，张斌，刘正伟，伍晓红，薛晓敏. 含双时滞振动主动控制系统超谐共振及亚谐共振分析[J]. 工程力学, 2010, 27(12): 84-89.
SUN Qing, ZHANG Bin, LIU Zheng-wei, WU Xiao-hong, XUE Xiao-min. Analysis of superharmonic and subharmonic resonance responses of active vibration control system with double time delay [J]. Engineering Mechanics, 2010, 27(12): 84-89.
[14]Nayfeh A H. Linear and nonlinear structure mechanics [M]. New York: Wiley Interscience, 2004.
[15]彭剑, 赵珧冰, 王连华. 时滞反馈及轴力作用下弹性梁的非线性振动[J]. 湖南大学学报(自然科学版), 2013, 40(9):30-36.
PENG Jian, ZHAO Yao-bing, WANG Lian-hua. Nonlinear vibrations of elastic beams subjected to axial force and delayed- feedback［J］. Journal of Hunan University (Naturnal Science), 2013, 40(9):30-36.