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  本文選題：微納米梁　切入點：幾何非線性　出處：《長沙理工大學(xué)》2015年碩士論文

【摘要】：近年來,微納機電系統(tǒng)(MEMS/NEMS)得到了快速的發(fā)展,作為MEMS/NEMS中的重要部件,MEMS/NEMS中微納米梁的力學(xué)特性研究成為了微納米力學(xué)的研究熱點之一。由于微納米梁的尺寸很小,導(dǎo)致其表現(xiàn)出不同于宏觀物體的力學(xué)性能,例如表面效應(yīng)、尺寸效應(yīng)等。同時,由于微器件在制造和使用過程中不可避免的會產(chǎn)生損傷。因此針對上述問題,本文主要進(jìn)行以下研究:首先,在考慮微納米梁幾何非線性、損傷效應(yīng)、表面效應(yīng)以及尺寸效應(yīng)基礎(chǔ)上,基于Euler-Bernoulli梁理論與哈密爾頓原理建立了具有損傷微納米梁的非線性運動控制方程。然后運用伽遼金法將非線性偏微分方程轉(zhuǎn)化為非線性常微分方程,并利用諧波平衡法對其進(jìn)行求解。利用數(shù)值分析方法,討論結(jié)構(gòu)尺寸、表面效應(yīng)、外載電壓等參數(shù)對微納米梁非線性振動特性的影響。接著,在考慮范德華力、壓電效應(yīng)、幾何非線性、表面效應(yīng)、損傷效應(yīng)以及尺寸效應(yīng)基礎(chǔ)上,基于Euler-Bernoulli梁理論與哈密爾頓原理建立了具有損傷微納米梁非線性運動控制方程。然后通過伽遼金法和四階龍格庫塔法對微納米梁的控制方程進(jìn)行求解。討論并分析了結(jié)構(gòu)尺寸、損傷變量以及壓電電壓等參數(shù)對壓電微納米梁坍塌行為的影響.最后,在考慮壓電效應(yīng)、幾何非線性、表面效應(yīng)、損傷效應(yīng)以及尺寸效應(yīng)基礎(chǔ)上,基于Euler-Bernoulli梁理論建立微納米梁模型,并在模型上下層施加反相位電載荷,對微納米梁的非線性動力學(xué)特性進(jìn)行分析研究。然后通過哈密爾頓原理得到了微納米梁的Duffing方程,并利用伽遼金法以及四階龍格庫塔法對其進(jìn)行數(shù)值求解。討論并分析了阻尼、壓電電壓、外載電壓以及損傷變量等參數(shù)對微納米梁分岔與混沌的影響。
[Abstract]:In recent years, the MEMS / NEMS has been developed rapidly. As an important part of MEMS/NEMS, the study on the mechanical properties of micro / nano beam has become one of the hotspots in the field of micro / nano mechanics.Due to the small size of the micro-and nano-beam, it shows different mechanical properties from macroscopic objects, such as surface effect, size effect and so on.At the same time, the damage of microdevices is inevitable in the process of manufacture and use.Therefore, this paper mainly studies the following problems: firstly, on the basis of considering the geometric nonlinearity, damage effect, surface effect and size effect of micro and nano-beam,Based on the Euler-Bernoulli beam theory and Hamilton principle, the nonlinear motion control equations of a micro and nano beam with damage are established.Then the Galerkin method is used to transform the nonlinear partial differential equation into the nonlinear ordinary differential equation, and the harmonic balance method is used to solve it.The effects of structural size, surface effect and external load voltage on the nonlinear vibration characteristics of micro and nano-beam are discussed by numerical analysis.Then, on the basis of considering van der Waals force, piezoelectric effect, geometric nonlinearity, surface effect, damage effect and size effect, the nonlinear motion governing equation of micro-nanometer beam with damage is established based on Euler-Bernoulli beam theory and Hamilton principle.Then, Galerkin method and fourth order Runge-Kutta method are used to solve the governing equation of micro and nano beam.The effects of structural dimensions, damage variables and piezoelectric voltage on the collapse behavior of piezoelectric microbeams are discussed and analyzed.Finally, on the basis of considering the piezoelectric effect, geometric nonlinearity, surface effect, damage effect and size effect, the model of micro-nanometer beam is established based on Euler-Bernoulli beam theory, and the anti-phase electric load is applied to the upper and lower layers of the model.The nonlinear dynamic characteristics of micro-and nano-beam are analyzed and studied.Then the Duffing equation of the micro and nanometer beam is obtained by Hamilton principle and solved numerically by Galerkin method and fourth order Runge-Kutta method.The effects of damping, piezoelectric voltage, external load voltage and damage variables on the bifurcation and chaos of micro-nanometer beam are discussed and analyzed.
【學(xué)位授予單位】：長沙理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TB383.1

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