纳米梁非线性振动反馈控制研究

发布时间：2018-10-25 12:26

【摘要】：纳米梁作为微纳机电系统器件的基础元件,具有尺寸小、质量轻和灵敏度高等优点,被成功应用于汽车工业、医疗、军事等领域,成为科研工作者研究的热点问题之一。然而随着结构尺寸缩小至纳米量级,其振动行为容易从线性区进入非线性区,出现多值、分岔等非线性行为,这些不稳定因素将影响微机电系统(Micro Electromechanical System,MEMS)、纳机电系统(Nano Electromechanical System,NEMS)工作的稳定性,阻碍了MEMS/NEMS技术的发展。因此,研究纳米梁非线性振动的影响因素及控制方法,对进一步了解和认识微纳机电系统,完善并制造出具有新功能的MEMS/NEMS元件具有重要意义。本文以两端固支的欧拉-伯努力梁为振动模型,应用理论分析和数值模拟相结合的方法,分析了电容控制器和压电控制器对静电激励纳米梁非线性振动的控制效果。首先,建立两端固支静电激励纳米梁电容控制模型。平行板电容器电容值随纳米梁振动发生变化,电容式传感器根据电容变化提取振动信号,并将放大后的振动信号传递到控制器作为控制信号实现纳米梁的非线性振动控制。通过哈密顿原理得到纳米梁非线性振动控制方程,利用多尺度法得到系统幅频响应方程及相频响应方程,进行稳定性分析。通过幅频特性响应分析得到系统参数和控制参数对纳米梁振动稳定性和最大振幅的影响规律。在电容控制器作用下,实现了纳米梁的稳态振动。其次,研究考虑轴向力作用时纳米梁非线性振动的压电控制。应用瑞利黎兹法研究初始轴向力与系统固有频率的关系。建立含有轴向力和压电控制力的非线性控制微分方程。应用多尺度法分析非线性方程的一阶近似解,得到非线性振动系统主共振和超谐共振的幅频响应方程和相频响应方程。分析幅频响应曲线得到激励电压、阻尼、反馈增益参数及轴向力对纳米梁非线性振动稳定性及最大振幅的影响,通过压电控制能够抑制纳米梁的非线性振动。最后,分别考虑卡西米尔力和范德瓦尔斯力作用,研究纳米梁非线性振动的压电控制。利用多尺度法分析了纳尺度力作用下系统参数和控制参数对纳米梁非线性振动稳定性及最大振幅的影响。本文研究表明,压电控制器和电容控制器对纳米梁非线性振动具有良好的控制作用。通过合理选取控制参数和系统参数,能够削弱甚至抑制纳米梁的非线性振动,该研究结果为控制微纳机电系统非线性振动提供了新的理论方法,具有一定的理论意义和工程应用价值。
[Abstract]:As the basic components of micro / nano electromechanical system devices, nanoscale beams have been successfully applied in automobile industry, medical treatment, military and other fields, and have become one of the hot issues in the research of researchers because of their small size, light weight and high sensitivity. However, as the size of the structure shrinks to nanometer order, the vibration behavior of the structure tends to move from the linear region to the nonlinear region, resulting in nonlinear behavior such as multi-value, bifurcation and so on. These unstable factors will affect the stability of (Nano Electromechanical System,NEMS (MEMS (Micro Electromechanical System,MEMS), and hinder the development of MEMS/NEMS technology. Therefore, it is of great significance to study the influence factors and control methods of nonlinear vibration of nano-beam, to further understand and understand the micro-nano electromechanical system, and to perfect and manufacture the MEMS/NEMS elements with new functions. In this paper, an Euler-Bergh beam with fixed ends is used as the vibration model, and the control effect of capacitive controller and piezoelectric controller on the nonlinear vibration of electrostatic excited nano-beam is analyzed by using the method of theoretical analysis and numerical simulation. First of all, the capacitance control model of the nanoscale beam excited by electrostatic clamping at both ends is established. The capacitance of parallel plate capacitors varies with the vibration of the nano-beam. The capacitive sensor extracts the vibration signal according to the change of the capacitance, and transmits the amplified vibration signal to the controller as the control signal to realize the nonlinear vibration control of the nano-beam. The nonlinear vibration control equations of nanoscale beams are obtained by Hamiltonian principle. The amplitude-frequency response equations and phase frequency response equations of the system are obtained by using the multi-scale method, and the stability analysis is carried out. The effects of system parameters and control parameters on the vibration stability and maximum amplitude of nanoscale beams are obtained by analyzing the amplitude-frequency response. The steady-state vibration of the nanoscale beam is realized under the action of capacitive controller. Secondly, piezoelectric control of nonlinear vibration of nano-beam considering axial force is studied. The relationship between the initial axial force and the natural frequency of the system is studied by using the Rayleigh method. A nonlinear governing differential equation with axial force and piezoelectric control force is established. The first order approximate solution of nonlinear equation is analyzed by multi-scale method. The amplitude-frequency response equation and phase frequency response equation of main resonance and super harmonic resonance of nonlinear vibration system are obtained. The effects of excitation voltage, damping, feedback gain parameters and axial force on the nonlinear vibration stability and maximum amplitude of nano-beam are analyzed. The nonlinear vibration of nano-beam can be suppressed by piezoelectric control. Finally, the piezoelectric control of nonlinear vibration of a nanoscale beam is studied by considering the Casimir force and van der Waals force respectively. The effects of system parameters and control parameters on the nonlinear vibration stability and maximum amplitude of nanoscale beams under nanoscale force are analyzed by multi-scale method. The results show that the piezoelectric controller and the capacitor controller have good control effect on the nonlinear vibration of the nanoscale beam. The nonlinear vibration of nano-beam can be weakened or even suppressed by selecting control parameters and system parameters. The results provide a new theoretical method for the control of nonlinear vibration of micro-nano electromechanical system. It has certain theoretical significance and engineering application value.
【学位授予单位】：山东理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB535;O322

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