納米梁非線性振動反饋控制研究
發(fā)布時間：2018-10-25 12:26
【摘要】：納米梁作為微納機電系統(tǒng)器件的基礎元件,具有尺寸小、質(zhì)量輕和靈敏度高等優(yōu)點,被成功應用于汽車工業(yè)、醫(yī)療、軍事等領域,成為科研工作者研究的熱點問題之一。然而隨著結(jié)構尺寸縮小至納米量級,其振動行為容易從線性區(qū)進入非線性區(qū),出現(xiàn)多值、分岔等非線性行為,這些不穩(wěn)定因素將影響微機電系統(tǒng)(Micro Electromechanical System,MEMS)、納機電系統(tǒng)(Nano Electromechanical System,NEMS)工作的穩(wěn)定性,阻礙了MEMS/NEMS技術的發(fā)展。因此,研究納米梁非線性振動的影響因素及控制方法,對進一步了解和認識微納機電系統(tǒng),完善并制造出具有新功能的MEMS/NEMS元件具有重要意義。本文以兩端固支的歐拉-伯努力梁為振動模型,應用理論分析和數(shù)值模擬相結(jié)合的方法,分析了電容控制器和壓電控制器對靜電激勵納米梁非線性振動的控制效果。首先,建立兩端固支靜電激勵納米梁電容控制模型。平行板電容器電容值隨納米梁振動發(fā)生變化,電容式傳感器根據(jù)電容變化提取振動信號,并將放大后的振動信號傳遞到控制器作為控制信號實現(xiàn)納米梁的非線性振動控制。通過哈密頓原理得到納米梁非線性振動控制方程,利用多尺度法得到系統(tǒng)幅頻響應方程及相頻響應方程,進行穩(wěn)定性分析。通過幅頻特性響應分析得到系統(tǒng)參數(shù)和控制參數(shù)對納米梁振動穩(wěn)定性和最大振幅的影響規(guī)律。在電容控制器作用下,實現(xiàn)了納米梁的穩(wěn)態(tài)振動。其次,研究考慮軸向力作用時納米梁非線性振動的壓電控制。應用瑞利黎茲法研究初始軸向力與系統(tǒng)固有頻率的關系。建立含有軸向力和壓電控制力的非線性控制微分方程。應用多尺度法分析非線性方程的一階近似解,得到非線性振動系統(tǒng)主共振和超諧共振的幅頻響應方程和相頻響應方程。分析幅頻響應曲線得到激勵電壓、阻尼、反饋增益參數(shù)及軸向力對納米梁非線性振動穩(wěn)定性及最大振幅的影響,通過壓電控制能夠抑制納米梁的非線性振動。最后,分別考慮卡西米爾力和范德瓦爾斯力作用,研究納米梁非線性振動的壓電控制。利用多尺度法分析了納尺度力作用下系統(tǒng)參數(shù)和控制參數(shù)對納米梁非線性振動穩(wěn)定性及最大振幅的影響。本文研究表明,壓電控制器和電容控制器對納米梁非線性振動具有良好的控制作用。通過合理選取控制參數(shù)和系統(tǒng)參數(shù),能夠削弱甚至抑制納米梁的非線性振動,該研究結(jié)果為控制微納機電系統(tǒng)非線性振動提供了新的理論方法,具有一定的理論意義和工程應用價值。
[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.
【學位授予單位】：山東理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TB535;O322
本文編號：2293691
[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.
【學位授予單位】：山東理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TB535;O322
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