学术论文

      静电激励纳米梁超谐共振电容控制

      Capacitance control of nanobeam with electrostatically actuated excitation for superharmonic resonance

      摘要:
      为研究静电激励纳米梁非线性振动的超谐共振控制问题,以Euler-Bernoulli梁为模型,提出一种非线性振动电容控制方法.纳米梁平行板电容器形成于纳米梁与平行极板间,其电容值随纳米梁的振动而变化,电容式传感器根据电容变化提取振动信号、产生控制电压.控制电压作为控制信号输入控制器控制纳米梁的非线性振动.应用多尺度法求得系统超谐共振的幅频响应方程,分析了振动方程解的稳定性,以及交流激励电压幅值、阻尼、反馈增益参数对系统振动稳定性及振幅的影响规律.应用数值分析方法得到纳米梁振动稳定性与纳米梁参数之间的关系,求得振动响应的稳定解.结果显示:当无量纲阻尼由0.017 5增大至0.020 3或是激励电压幅值减小至1.8 V时,最大振幅分别衰减40%和50%左右;增大阻尼和反馈增益参数能够削弱甚至消除纳米梁超谐振动的非线性特性.该研究结果为控制纳机电系统非线性振动提供了一种新的理论方法.
      Abstract:
      A capacitive control method of nonlinear vibration was present for the problem of nonlinear vibration control of nanobeam electrostatically actuated for superharmonic resonance by using the model of Euler-Bernoulli beam.The capacitance of nanobeam capacitor formed between the nanobeam and the grounded substrate, which changed with nanobeam vibration.The capacitive sensor was applied to extract vibration signals according to the change of capacitance and to generate control voltage to control the nonlinear vibration of nanobeam via controller.The multiple scales method was applied to obtain the amplitude-frequency equation for superharmonic resonance and the stability of vibration equation solutions was analyzed.The influences of the amplitude of alternating excitation voltage, damping and the parameters of feedback gains on the system vibration stability and the amplitudes were analyzed.The relationship between the stability of the nanobeam vibration and the nanobeam parameters was obtained by using the method of numerical analysis, the stable solutions of the vibration response were solved.The results shown that the peak amplitude was suppressed about 40% and 50% respectively, when the dimensionless damping increased from 0.017 5 to 0.020 3 or the amplitude of excitation voltage reduced to 1.8 V.The nonlinear vibration characters of nanobeam for superharmonic resonance can be weakened or eliminated by enlarging the values of damping and parameters of feedback gains.The results of this study provided a new theoretical method for the nonlinear vibration control of nano electromechanical systems.
      Author: GONG Qing-mei XU Ying-zi LIU Can-chang ZHOU Chang-cheng MA Chi-cheng JIANG Rui-rui
      作者单位: 山东理工大学交通与车辆工程学院,山东淄博,255049
      年,卷(期): 2017, 42(2)
      分类号: O322
      在线出版日期: 2017年5月16日
      基金项目: 国家自然科学基金资助项目