纳米梁非线性振动隧道电流反馈控制
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摘要
针对纳米梁振动中出现的非线性问题,提出了基于隧道电流反馈控制的纳米梁振动控制方法。将电子隧道效应理论应用于纳米梁的振动信号检测中,以提高信号提取的准确性,通过位移和速度两种电流反馈所产生的两种控制电压信号对纳米梁非线性振动进行控制,建立基于隧道电流反馈控制的纳米梁主共振非线性振动方程,并应用多尺度方法求得主共振幅频响应方程,研究了直流和交流激励电压、振动控制参数、阻尼值、控制电压等与纳米梁主共振幅频响应之间的关系,分析了影响系统振动非线性的因素。研究结果表明,减小直流激励电压至1. 5 V或交流激励电压降至1. 0 V,系统振幅峰值分别衰减50%和58%,振动非线性减弱;增大阻尼、减小系统控制电压以及选择适当的振动控制参数均可以使纳米梁主共振幅频响应得到有效控制,同时可以降低系统振动的非线性。
A vibration control method based on tunnel current feedback control was proposed to solve nonlinear problems of nanobeam vibration. The theory of electron tunneling effect was applied to the vibration signal detection of nanobeam for improving the accuracy of signal extraction. The nonlinear vibration of nanobeam was controlled by two kinds of control voltage signals generated by displacement and velocity current feedback. The nonlinear vibration equation of nanobeam based on tunnel current feedback control was established,and the amplitude-frequency response equation of primary resonance was solved by multi-scale method. The relationship of primary resonance amplitude frequency response of nanobeam with direct current excitation voltage,alternating current excitation voltage,vibration control parameter,damping and control voltage was studied,and the factors affecting vibration nonlinearity of the system were analyzed. The results show that when the direct current excitation voltage is reduced to 1. 5 V or the alternating current excitation voltage isreduced to 1. 0 V,the peak amplitudes of the system are damped by 50 % and 58 %,respectively,and the vibration nonlinearity of the system is weakened. The primary resonance amplitudefrequency response of nanobeam can be effectively controlled by increasing damping,reducing the control voltage of the system and selecting appropriate vibration control parameters, and the nonlinear vibration of the system can be controlled.
A vibration control method based on tunnel current feedback control was proposed to solve nonlinear problems of nanobeam vibration. The theory of electron tunneling effect was applied to the vibration signal detection of nanobeam for improving the accuracy of signal extraction. The nonlinear vibration of nanobeam was controlled by two kinds of control voltage signals generated by displacement and velocity current feedback. The nonlinear vibration equation of nanobeam based on tunnel current feedback control was established,and the amplitude-frequency response equation of primary resonance was solved by multi-scale method. The relationship of primary resonance amplitude frequency response of nanobeam with direct current excitation voltage,alternating current excitation voltage,vibration control parameter,damping and control voltage was studied,and the factors affecting vibration nonlinearity of the system were analyzed. The results show that when the direct current excitation voltage is reduced to 1. 5 V or the alternating current excitation voltage isreduced to 1. 0 V,the peak amplitudes of the system are damped by 50 % and 58 %,respectively,and the vibration nonlinearity of the system is weakened. The primary resonance amplitudefrequency response of nanobeam can be effectively controlled by increasing damping,reducing the control voltage of the system and selecting appropriate vibration control parameters, and the nonlinear vibration of the system can be controlled.
引文
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[14] GONG Q M,LIU C C,XU Y Z,et al. Nonlinear vibration control with nanocapacitive sensor for electrostatically actuated nanobeam[J]. Journal of Low Frequency Noise Vibration and Active Control,2018,37(2):235-252.
[15]巩庆梅,许英姿,刘灿昌,等.静电激励纳米梁超谐共振电容控制[J].广西大学学报(自然科学版),2017,42(2):461-469.
[16]巩庆梅,许英姿,刘灿昌,等.主共振纳米梁非线性振动电容控制[J].科学技术与工程,2017,17(18):142-148.
[17] BENI Y T,KOOCHI A,ABADYAN M. Theoretical study of the effect of Casimir force,elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS[J]. Physica E:Low-dimensional Systems and Nanostructures,2011,43(4):979-988.
[18] WANG Y Z. Nonlinear internal resonance of double-walled nanobeams under parametric excitation by nonlocal continuum theory[J]. Applied Mathematical Modelling,2017,48:621-634.
[19] ALVES M,RIBEIRO P. Non-linear modes of vibration of Timoshenko nanobeams under electrostatic actuation[J]. International Journal of Mechanical Sciences,2017,130:188-202.
[20] LIU C,黄庆安.微机电系统基础[M].北京:机械工业出版社,2013:231-244.
[21]刘延柱,陈立群,陈文良.振动力学[M].北京:高等教育出版社,2011:206-211.
[22]巩庆梅.纳米梁非线性振动反馈控制研究[D].淄博:山东理工大学,2017.
[2]徐毓龙.纳米级隧道效应器件——双电子层隧道晶体管和共振隧道二极管[J].电子产品世界,2001,13(10):53-54.
[3]罗源源,刘俊,李锦明.正交梁式隧道效应微机械陀螺仪的设计与仿真[J].传感技术学报,2007,20(2):317-320.
[4] 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.
[5] 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.
[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.
[7]李梦超,傅星,魏小雷,等.基于隧道效应的纳米级振动传感器的研究[J].压电与声光,2004,26(6):464-466.
[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.
[9] DUMITRU I C,MARTIN K. On nonlinear response near-half natural frequency of electrostatically actuated microresonators[J]. International Journal of Structural Stability and Dynamics,2011,11(4):641-672.
[10] SHAHROKH H,REZA N. An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects[J]. Composites Part B:Engineering,2013,52(4):199-206.
[11] ZHAO D M,LIU J L,WANG L. Nonlinear free vibration of a cantilever nanobeam with surface effects:Semi-analytical solutions[J]. International Journal of Mechanical Sciences,2016,113:184-195.
[12]杨晓东,林志华.利用多尺度方法分析基于非局部效应纳米梁的非线性振动[J].中国科学(技术科学),2010,40(2):152-156.
[13]刘灿昌,裘进浩,季宏丽,等.考虑非局部效应的纳米梁非线性振动[J].振动与冲击,2013,32(4):158-162.
[14] GONG Q M,LIU C C,XU Y Z,et al. Nonlinear vibration control with nanocapacitive sensor for electrostatically actuated nanobeam[J]. Journal of Low Frequency Noise Vibration and Active Control,2018,37(2):235-252.
[15]巩庆梅,许英姿,刘灿昌,等.静电激励纳米梁超谐共振电容控制[J].广西大学学报(自然科学版),2017,42(2):461-469.
[16]巩庆梅,许英姿,刘灿昌,等.主共振纳米梁非线性振动电容控制[J].科学技术与工程,2017,17(18):142-148.
[17] BENI Y T,KOOCHI A,ABADYAN M. Theoretical study of the effect of Casimir force,elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS[J]. Physica E:Low-dimensional Systems and Nanostructures,2011,43(4):979-988.
[18] WANG Y Z. Nonlinear internal resonance of double-walled nanobeams under parametric excitation by nonlocal continuum theory[J]. Applied Mathematical Modelling,2017,48:621-634.
[19] ALVES M,RIBEIRO P. Non-linear modes of vibration of Timoshenko nanobeams under electrostatic actuation[J]. International Journal of Mechanical Sciences,2017,130:188-202.
[20] LIU C,黄庆安.微机电系统基础[M].北京:机械工业出版社,2013:231-244.
[21]刘延柱,陈立群,陈文良.振动力学[M].北京:高等教育出版社,2011:206-211.
[22]巩庆梅.纳米梁非线性振动反馈控制研究[D].淄博:山东理工大学,2017.
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