考虑损伤微纳米梁的非线性动力学分析

发布时间：2018-04-09 02:02

本文选题：微纳米梁　切入点：几何非线性　出处：《长沙理工大学》2015年硕士论文

【摘要】：近年来,微纳机电系统(MEMS/NEMS)得到了快速的发展,作为MEMS/NEMS中的重要部件,MEMS/NEMS中微纳米梁的力学特性研究成为了微纳米力学的研究热点之一。由于微纳米梁的尺寸很小,导致其表现出不同于宏观物体的力学性能,例如表面效应、尺寸效应等。同时,由于微器件在制造和使用过程中不可避免的会产生损伤。因此针对上述问题,本文主要进行以下研究:首先,在考虑微纳米梁几何非线性、损伤效应、表面效应以及尺寸效应基础上,基于Euler-Bernoulli梁理论与哈密尔顿原理建立了具有损伤微纳米梁的非线性运动控制方程。然后运用伽辽金法将非线性偏微分方程转化为非线性常微分方程,并利用谐波平衡法对其进行求解。利用数值分析方法,讨论结构尺寸、表面效应、外载电压等参数对微纳米梁非线性振动特性的影响。接着,在考虑范德华力、压电效应、几何非线性、表面效应、损伤效应以及尺寸效应基础上,基于Euler-Bernoulli梁理论与哈密尔顿原理建立了具有损伤微纳米梁非线性运动控制方程。然后通过伽辽金法和四阶龙格库塔法对微纳米梁的控制方程进行求解。讨论并分析了结构尺寸、损伤变量以及压电电压等参数对压电微纳米梁坍塌行为的影响.最后,在考虑压电效应、几何非线性、表面效应、损伤效应以及尺寸效应基础上,基于Euler-Bernoulli梁理论建立微纳米梁模型,并在模型上下层施加反相位电载荷,对微纳米梁的非线性动力学特性进行分析研究。然后通过哈密尔顿原理得到了微纳米梁的Duffing方程,并利用伽辽金法以及四阶龙格库塔法对其进行数值求解。讨论并分析了阻尼、压电电压、外载电压以及损伤变量等参数对微纳米梁分岔与混沌的影响。
[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.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB383.1

【参考文献】