共查询到19条相似文献,搜索用时 171 毫秒
1.
基于三维组装技术的可延展结构具备优异的延展性和可调控性,使其成功应用于各类可延展电子器件的制备中。为了评估该类电子器件的稳定性,本文研究三维波纹型可延展结构的振动行为。首先,基于非线性的Euler-Bernoulli梁理论、Kelvin-Voigt粘弹性理论和考虑压电材料的表面压电效应,建立三维波纹结构的理论分析模型;其次,基于能量原理和扩展拉格朗日运动原理,推导出该结构的动力学控制方程;然后采用二级四阶辛Runge-Kutta求解该动力学方程。通过数值仿真实验验证了辛算法的优越性,同时,还发现随着三维波纹型可延展结构外界激励及其结构参数的变化,该结构的振动特性会从倍周期向分岔和混沌转化;本文结果为三维波纹型可延展结构的优化设计及应用提供理论基础。 相似文献
2.
基于岛-桥结构的柔性电子器件已被用于健康监测和皮肤电子等领域。但是柔性电子器件在工作中极易受工作温度变化等激励产生振动,进而影响器件的灵敏度与可靠性。因此本文研究在温度场作用下岛-桥结构屈曲薄膜的动力学问题。首先,基于Euler-Bernoulli梁理论,建立温度场作用下岛-桥结构屈曲薄膜的动力学控制方程。其次,通过引入新变量,将原动力学方程引入Hamilton体系中,得到相应的Hamilton正则方程。随后,采用辛Runge-Kutta方法求解该Hamilton正则方程,并与经典Runge-Kutta方法对比,数值结果显示了辛算法在求解非线性动力学方程时高精度、高数值稳定性的优势,进一步讨论了温度变化量、预应变、阻尼系数等对屈曲薄膜动力学响应的影响。本文研究为柔性电子器件动力学设计提供了理论参考。 相似文献
3.
硬薄膜/软基底结构的表面失稳问题一直是柔性电子器件的难题,基于此,本文考虑了双层结构与弹性梯度基底间的界面剪切力,建立了双层薄膜/弹性梯度基底模型;利用位移协调条件,理论推导得到了双层薄膜/弹性梯度基底结构的临界应变和失稳波长的表达式并通过有限元仿真,验证了本研究解析解的有效性。在此基础上,应用此解析解进一步研究了弹性梯度基底的材料、双层薄膜结构厚度比等参数对临界应变和波长的影响。结果表明:减小器件层的厚度或者增加封装层的厚度,可以提高双层膜/弹性梯度基底结构的稳定性;当弹性梯度材料基底表面“较软”或器件层“较硬”时,器件层与基底界面的剪切力的影响较大,可以提升三层膜/基结构抵抗界面破坏的能力。本研究成果将为硬薄膜/弹性梯度基底结构的柔性电子器件的制备提供理论支撑。 相似文献
4.
当上层超弹性硬质薄膜和下层可膨胀基底构成的双层结构受压时,薄膜的自由表面可通过形成褶皱降低系统能量.研究表明,上下两层的模量比不同时,上层弹性硬质薄膜将表现出不同的表面失稳模式.本文提出了一种新颖的方法可有效抑制双层软材料的表面失稳,即改变基底材料的泊松比,这种方法同时适用于不具有应变硬化的软材料.首先基于Neo-Hookean模型发展了小变形条件下双层结构表面失稳的理论模型,通过半解析的方法得到了表面失稳的临界应变;然后通过有限元计算与模拟,进一步验证了负泊松比基底可延缓表面失稳.结果表明:(1)当双层结构基底泊松比为正且趋于0.5(不可压缩)时,双层结构在较小的压缩应变下出现表面失稳;(2)当基底的泊松比为负且趋于-1时,可被压缩至46%而不出现表面失稳,即可膨胀基底能有效抑制薄膜的表面失稳.本文发展的方法及主要结果可为延展性电子器件的设计提供指导. 相似文献
5.
辛弹性力学已广泛应用于弹性学中各种边值问题的精确解、计算表面波模式以及预测多层超弹性薄膜中的表面褶皱。本文展示了辛分析框架还可应用于受约束介电弹性体中的表面褶皱。机械和电位移向量是两个基本变量来描述介电弹性体中机械变形与电场紧密耦合。褶皱的临界电压可以通过引入基本变量的对偶变量来从辛本征值问题中解决。本文采用扩展的W-W(Wittrick-Williams)算法和精确的积分方法,准确而高效地解决制定的辛本征值问题的本征值。通过将褶皱电压和波数与有无表面能的褶皱基准结果进行比较,验证了辛分析的有效性。辛分析框架简洁且适用于其他不稳定问题,如分层电介质弹性体、磁弹性不稳定性以及层压复合结构的微观和宏观不稳定性。 相似文献
6.
7.
8.
9.
超细长弹性杆动力学研究在DNA的平衡、稳定性等问题的研究中有重要的应用。为了便于超细长弹性杆动力学研究中数值结果图形后处理以及研究表面接触等问题的需要,需要建立弹性杆的表面模型和相应算法。本文利用Kirchhoff弹性杆模型的动力学比拟技巧,建立了描述超细长弹性杆曲面的常微分/积分方程组,利用Adames方法和递推方法设计了方程的数值解法,并给出了超长弹性杆的数值仿真结果的图形处理的计算实例。 相似文献
10.
本文采用弹性理论,研究了鼓泡法试验过程中,外力(P)与薄膜中心挠度(w_0)之间的本构关系,计算出P与w_0的数学表达式.该分析模型考虑了薄膜内延展变形及薄膜中残余拉应力对本构关系的影响,并在较大挠曲区间范围内(挠度为10~(-2)~10~2倍薄膜厚度)分析本构关系特征.分析结果表明,外力与薄膜中心挠度之间本构关系可表示为:P∝w_0~n,n为指数.随着薄膜中心挠度的增加,薄膜的主要力学行为由弯曲过渡到延展,本构关系由线性过渡到立方关系,本构关系方程指数n由1增加到3.利用本构方程进行数值计算结果表明,薄膜挠曲所需外力随着薄膜半径增加而减小,随着残余拉应力的增加而增加.相对于以往不考虑延展变形的小挠度模型,本文所提出的力学模型更适合于大挠度条件下鼓泡法试验. 相似文献
11.
In this study, a unified nonlinear dynamic buckling analysis for Euler–Bernoulli beam–columns subjected to constant loading rates is proposed with the incorporation of mercurial damping effects under thermal environment. Two generalized methods are developed which are competent to incorporate various beam geometries, material properties, boundary conditions, compression rates, and especially, the damping and thermal effects. The Galerkin–Force method is developed by implementing Galerkin method into force equilibrium equations. Then for solving differential equations, different buckled shape functions were introduced into force equilibrium equations in nonlinear dynamic buckling analysis. On the other hand, regarding the developed energy method, the governing partial differential equation for dynamic buckling of beams is also derived by meticulously implementing Hamilton’s principles into Lagrange’s equations. Consequently, the dynamic buckling analysis with damping effects under thermal environment can be adequately formulated as ordinary differential equations. The validity and accuracy of the results obtained by the two proposed methods are rigorously verified by the finite element method. Furthermore, comprehensive investigations on the structural dynamic buckling behavior in the presence of damping effects under thermal environment are conducted. 相似文献
12.
13.
M. Faghih Shojaei R. Ansari V. Mohammadi H. Rouhi 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(3):421-440
A numerical solution methodology is proposed herein to investigate the nonlinear forced vibrations of Euler–Bernoulli beams with different boundary conditions around the buckled configurations. By introducing a set of differential and integral matrix operators, the nonlinear integro-differential equation that governs the buckling of beams is discretized and then solved using the pseudo-arc-length method. The discretized governing equation of free vibration around the buckled configurations is also solved as an eigenvalue problem after imposing the boundary conditions and some complicated matrix manipulations. To study forced and nonlinear vibrations that take place around a buckled configuration, a Galerkin-based numerical method is applied to reduce the partial integro-differential equation into a time-varying ordinary differential equation of Duffing type. The Duffing equation is then discretized using time differential matrix operators, which are defined based on the derivatives of a periodic base function. Finally, for any given magnitude of axial load, the pseudo -arc-length method is used to obtain the nonlinear frequencies of buckled beams. The effects of axial load on the free vibration, nonlinear, and forced vibrations of beams in both prebuckling and postbuckling domains for the lowest three vibration modes are analyzed. This study shows that the nonlinear response of beams subjected to periodic excitation is complex in the postbuckling domain. For example, the type of boundary conditions significantly affects the nonlinear response of the postbuckled beams. 相似文献
14.
梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳,对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理,建立了横向载荷作用下轴向运动梁的动力学方程,获得了梁的后屈曲构型。使用截断Galerkin法,将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明,后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式,获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外,轴向外激励的方向也会改变系统固有频率。 相似文献
15.
The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation. 相似文献
16.
S. Tomasiello 《Nonlinear dynamics》2007,50(1-2):37-48
In this paper, the nonlinear planar response of a hinged–hinged buckled beam to a primary-resonance excitation of its first
vibration mode is computed by a new numerical scheme. The beam is subjected to an axial force beyond the critical load of
the first buckling mode and to a transverse harmonic excitation. The nonlinear dynamical problem is solved by deducing directly
the discretized equations governing the problem thanks to a new approach, here called DQ based approach, since it is based
on the application of the quadrature rules of the DQM. As it will be shown, for the problem here considered, the minimum number
of degrees of freedom to be retained to limit the numerical errors is four. Computer simulations of the dynamic behaviour
of the discretized system are conducted by means of the IDQ method, a method proposed and recently generalized by the author.
A sequence of supercritical period-doubling bifurcations leading to chaos, snapthrough motions and quasi-periodic motions
can be observed, similarly to some cases existing in literature. 相似文献
17.
基底上薄膜结构中的过大残余压应力常常通过屈曲不稳定性诱发薄膜结构和功能的失效。屈曲不稳定性、演化与斑图形成是近年来非线性力学研究的热点。此类屈曲不稳定性受薄膜-基底的力学性质以及界面相互作用影响,进而呈现出复杂的屈曲模式如褶皱、翘曲和折痕等。论文简要综述褶皱、翘曲和折痕等屈曲模式的形成机制、影响因素和后屈曲形貌相关方面的进展。褶皱部分,重点介绍了褶皱的形成、多级褶皱结构、局域化的褶皱、各向异性褶皱和曲面上的褶皱。翘曲部分,介绍了翘曲结构包括一维翘曲结构、“电话线”屈曲泡,网络状屈曲泡等的形成与生长过程,并讨论了曲面几何、界面滑移、开裂等因素的影响。折痕及其它复杂屈曲模式部分,介绍了折痕、叠痕及隆起失稳的形成机制与临界条件. 相似文献
18.
We present an exact solution for the postbuckling configurations of beams with fixed–fixed, fixed–hinged, and hinged–hinged
boundary conditions. We take into account the geometric nonlinearity arising from midplane stretching, and as a result, the
governing equation exhibits a cubic nonlinearity. We solve the nonlinear buckling problem and obtain a closed-form solution
for the postbuckling configurations in terms of the applied axial load. The critical buckling loads and their associated mode
shapes, which are the only outcome of solving the linear buckling problem, are obtained as a byproduct. We investigate the
dynamic stability of the obtained postbuckling configurations and find out that the first buckled shape is a stable equilibrium
position for all boundary conditions. However, we find out that buckled configurations beyond the first buckling mode are
unstable equilibrium positions. We present the natural frequencies of the lowest vibration modes around each of the first
three buckled configurations. The results show that many internal resonances might be activated among the vibration modes
around the same as well as different buckled configurations. We present preliminary results of the dynamic response of a fixed–fixed
beam in the case of a one-to-one internal resonance between the first vibration mode around the first buckled configuration
and the first vibration mode around the second buckled configuration. 相似文献
19.
联合载荷作用下简支矩形板的屈曲和过屈曲 总被引:1,自引:0,他引:1
本文研究了简支正交各向异性矩形板在两对板受中面压力作用下的屈曲和过屈曲性态,得到了载荷的稳定性区域,证明了临界载荷最多为二重的。利用多参数摄动方法求得临界载荷附近板的过屈曲状态的渐近解,分析了在二重临界载荷附近,当载荷按比例变化时,板的可能的过屈曲状态及其与参数的依赖关系。 相似文献