基于电子隧道效应的纳米梁非线性振动控制

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (7) : 28-34.

论文

基于电子隧道效应的纳米梁非线性振动控制

姜瑞瑞，刘灿昌，李磊，秦志昌，万磊，孔维旭，周长城

作者信息 +

Nonlinear vibration control for a nano-beam based on electron tunneling effect

JIANG Ruirui, LIU Canchang, LI Lei, QIN Zhichang, WAN Lei, KONG Weixu,ZHOU Changcheng

Author information +

文章历史 +

摘要

以Euler-Bornoulli梁为振动模型，提出了基于电子隧道效应的纳米梁非线性振动控制方法。隧道效应电流具有高灵敏性、高精确性的特点，可用于检测纳米梁的振动信号。应用位移和速度电压反馈控制器，考虑时滞反馈影响，建立基于隧道效应的纳米梁时滞非线性振动控制方程，应用多尺度方法得到纳米梁主共振的幅频响应方程。研究了直流和交流激励电压、控制增益和时滞等参数与纳米梁振动非线性之间的关系，分析了减弱系统非线性、增强系统稳定性的影响因素。研究结果表明，通过选择合适的控制增益和时滞，适当减小直流和交流激励电压幅值可以降低振动的非线性，提高系统的稳定性。

Abstract

A nonlinear vibration control method for a nano-beam based on electron tunneling effect was proposed taking Euler-Bernoulli beam as its vibration model. Tunneling effect currents with features of high sensitivity and high accuracy were used to detect vibration signals of the nano-beam. Using displacement and velocity voltage feedback controllers and considering effects of time delay feedback,the time delay nonlinear vibration control equation of the nano-beam based on tunneling effect was established. The amplitude-frequency response equation of the nano-beam’s main resonance was derived with the multi-scale method. The relations among the nano-beam’s nonlinear vibration and parameters,such as,direct-current and alternating one excitation voltages,control gain and time delay were studied,and influence factors to weaken the system nonlinearity and enhance the system stability were analyzed. The results showed that the vibration nonlinearity can be reduced and the system stability can be improved through choosing appropriate control gain and time delay,and properly reducing amplitudes of direct-current and alternating one excitation voltages.

导出引用

姜瑞瑞，刘灿昌，李磊，秦志昌，万磊，孔维旭，周长城. 基于电子隧道效应的纳米梁非线性振动控制[J]. 振动与冲击, 2019, 38(7): 28-34

JIANG Ruirui, LIU Canchang, LI Lei, QIN Zhichang, WAN Lei, KONG Weixu,ZHOU Changcheng. Nonlinear vibration control for a nano-beam based on electron tunneling effect[J]. Journal of Vibration and Shock, 2019, 38(7): 28-34

参考文献

[1] 张文明，孟光，周健斌，等. 参数激励下静电驱动MEMS共振传感器的非线性动力特性研究[J]. 力学季刊，2009, 30(1):44-48.
ZHANG Wen-ming, MENG Guang, ZHOU Jian-bin, et al. Nonlinear dynamic characteristics of electrostatically actuated MEMS resonant sensors under parametric excitation[J]. Chinese Quarterly of Mechanics, 2009, 30(1):44-48.
[2] 张文明，闫寒，彭志科，等. 微纳机械谐振器能量耗散机理研究进展[J]. 科学通报，2017, 62(19):2077-2093.
ZHANG Wen-ming, YAN Han, PENG Zhi-ke, et al. Research progress on energy dissipation mechanisms in micro-and nano-mechanical resonators[J]. Chinese Science Bulletin, 2017, 62(19):2077-2093.
[3] 宋震煜，于虹. 纳米梁非线性振动的动力学分析[J]. 微纳电子技术，2006, 43(3):145-149.
SONG Zhen-yu, YU Hong. Dynamic analysis for nonlinear vibration of nanobeam[J]. Micronanoelectronic Technology, 2006, 43(3):145-149.
[4] ZHAO De-min, LIU Jian-lin, WANG Lin. Nonlinear free vibration of a cantilever nanobeam with surface effects: Semi-analytical solutions[J]. International Journal of Mechanical Sciences, 2016, 113:184-195.
[5] Rockstad H K, Tang T K, Reynolds J K, et al. A miniature, high-sensitivity, electron tunneling accelerometer[J]. Sensors and Actuators A: Physical, 1996, 53(1–3):227-231.
[6] 李梦超，傅星，胡小唐. 基于隧道效应的纳米级振动检测及测量[J]. 电子测量与仪器学报，2008, 22(2):6-10.
LI Meng-chao, FU Xing, HU Xiao-tang. Measurement and detection of nano level vibration based on tunneling effect[J]. Journal of Electronic Measurement and Instrument, 2008, 22(2):6-10.
[7] LI Meng-chao, FU Xing, WEI Xiao-lei, et al. Vibration compensation for scanning tunneling microscope[J]. Semiconductor Photonics and Technology, 2003, 9(4):230-233.
[8] 夏一，杜纲，傅星. 隧道传感系统微位移机构的主从关联优化设计[J]. 机械工程学报，2012, 48(9):10-17.
XIA Yi, DU Gang, FU Xing. Leader-follower optimization design of micro-displacement mechanism based on the tunneling effect sensing system[J]. Journal of Mechanical Engineering, 2012, 48(9):10-17.
[9] 陈帆，傅星，李梦超. 基于隧道效应的振动检测反馈系统设计[J]. 河南科技大学学报:自然科学版，2008, 29(4):77-81.
CHEN Fan, FU Xing, LI Meng-chao. Design of nano-vibration Detection Feedback Control System Based on Tunelling Effect[J]. Journal of Henan University of Science and Technology, 2008, 29(4):77-81.
[10] Opacak N, Milanovic V, Radovanovic J. Transmission singularities in resonant electron tunneling through double complex potential barrier[J]. Quantum Physics, 2017, 381 (41):3542-3547.
[11] Opacak N, Milanovic V, Radovanovic J, et al. Infinite dwell time and group delay in resonant electron tunneling through double complex potential barrier[J]. Superlattices and Microstructures, 2017,112:415-421.
[12] LIU Can-chang, JI Hong-li, SUN Hui-yu, et al. Optimal delayed control of nonlinear vibration resonances of single degree of freedom system[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2014, 31(1):49-55.
[13] GONG Qing-mei, LIU Can-chang, XU Ying-zi, et al. Nonlinear vibration control with nanocapacitive sensor for electrostatically actuated nanobeam[J]. Journal of Low Frequency Noise Vibration and Active Control, 2017.
[14] Dumitru I. Caruntu, Martin Knecht. On nonlinear response near-half natural frequency of electrostatically actuated microresonators[J]. International Journal of Structural Stability and Dynamics, 2011, 11(04): 641-672.
[15] Rhoads J F, Shaw S W, Turner K L. The nonlinear response of resonant microbeam systems with purely-parametric electrostatic actuation[J]. Journal of Micromechanics and Microengineering, 2006, 16(5):890-899.
[16] Shaat M, Abdelkefi A. Material structure and size effects on the nonlinear dynamics of electrostatically-actuated nano-beams[J]. International Journal of Non-Linear Mechanics, 2017, 89:25-42.
[17] Najar F, El-Borgi S, Reddy J N, et al. Nonlinear nonlocal analysis of electrostatic nanoactuators[J]. Composite Structures, 2015, 120:117-128.
[18] Bornassi S, Haddadpour H, Bornassi S , et al. Nonlocal vibration and pull-in instability analysis of electrostatic carbon-nanotube based NEMS devices[J]. Sensors and Actuators A , 2017,266 ,185–196.
[19] 张舒，徐鉴. 时滞耦合系统非线性动力学的研究进展[J]. 力学学报，2017, 49(3):565-587.
ZHANG Shu, XU Jian. Review on nonlinear dynamics in systems with coulpling delays[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3):565-587.
[20] SUN Xiu-ting, Xu Jian. Vibration control of nonlinear Absorber-Isolator-Combined structure with time-delayed coupling[J]. International Journal of Non-Linear Mechanics, 2016, 83:48-58.
[21] LIU Can-chang, YUE Shu-chang, ZHOU Ji-lei. Piezoelectric optimal delayed feedback control for nonlinear vibration of beams[J]. Journal of Low Frequency Noise Vibration and Active Control, 2016, 35(1):25-38.
[22] 孙清，刘正伟，伍晓红，等. 含双时滞振动主动控制系统的稳定性分析[J]. 西安交通大学学报，2010, 44(1):112-116.
SUN Qing, LIU Zheng-wei, WU Xiao-hong, et al. Stability analysis of active vibration control system involving double time delays[J]. Journal of Xian Jiaotong University, 2010, 44(1):112-116.
[23] LIU Chang. 微机电系统基础[M]. 机械工业出版社，2013.
LIU Chang. Foundation of MEMS[M]. China Machine Press, 2013.
[24] 刘延柱，陈文良，陈立群. 振动力学.第2版[M]. 高等教育出版社，2011.