基于非线性光纤环镜的全光波长变换综述

介绍了非线性光纤环镜的基本原理,以及利用光束传输法对耦合非线性薛定谔方程组进行数值分析,研究并搭建了采用非线性光纤环境作为介质,实现波长变换的实验系统,经实验证明,非线性光纤环路境能够将2.5 G bit/s归零码光脉冲波长变换20 nm,也能同时实现两个波长的转换。     

非局域非线性克尔介质中的高阶光孤子

利用变分法求得非局域非线性克尔介质中的厄密非局域光孤子和拉盖尔非局域光孤子,其呈现的形式分别为矩形阵列结构和链状对称结构。对于厄密非局域光孤子,当输入功率低于某一上限时,其能够保持矩形对称阵列,当输入功率较高时,其矩形对称阵列演化为拉盖尔非局域孤子的环形链状结构。     

端面泵浦热传导各向异性激光棒温场特性研究

了解决LD端面泵浦热传导各向异性激光介质产生的热效应问题,建立了端面绝热、侧面冷却的Nd:YVO4晶体热模型。考虑到Nd:YVO4为热传导各向异性材料,而光纤耦合LD输出光束有着超高斯分布的特点,利用特征函数法和常数变异法得到了超高斯光束端面泵浦热传导各向异性激光介质温度场的一般解析表达式。并定量分析了超高斯泵浦光阶次、泵浦功率以及光斑尺寸对于Nd:YVO4晶体温度场的影响。新的各向异性介质热传导方程求解方法具有计算量小、精度高等特点。研究结果表明：若LD输出功率为30W,光学聚焦耦合器的传输效率为82%时,4阶超高斯光束端面泵浦掺钕离子质量分数为0.5%的Nd:YVO4晶体,泵浦面获得528.95C的最大温升。所得结果可用于LD端面泵浦热传导各向异性激光介质全固态激光器热稳腔的设计之中,对于提高激光器性能具有了理论指导作用。     

端面泵浦热传导各向异性激光棒的温度场

为了解决LD端面泵浦热传导各向异性激光介质产生的热效应问题,建立了端面绝热、侧面冷却的Nd:YVO_4晶体热模型.考虑到Nd:YVO_4为热传导各向异性材料,而光纤耦合LD输出光束有超高斯分布的特点,利用特征函数法和常数变异法得到了超高斯光束端面泵浦热传导各向异性激光介质温度场的一般解析表达式,并定量分析了超高斯泵浦光阶次、泵浦功率以及光斑尺寸对Nd:YVO_4晶体温度场的影响.研究结果表明,若LD输出功率为50 W,光学聚焦耦合器的传输效率为82%,用四阶超高斯光束端面泵浦掺钕离子质量分数为0.5%的Nd:YVO_4晶体时,泵浦面可获得528.95 ℃的最大温升.所得结果可用于LD端面泵浦热传导各向异性激光介质全固态激光器热稳腔的设计,对于提高激光器性能具有理论指导作用.     

对边固支对边自由边界下复合材料层合板的解析解

在状态空间理论体系下,研究四边简支层合板壳精确解的文献比较多,而关于其它边界条件问题的文献却不是很多见。以边界位移函数方法为基础,推导了对边固支对边自由矩形层合板的非齐次状态方程,并给出了求解该方程时满足边界条件的控制方程。将非齐次状态方程增维齐次化后可避免积分时可能出现的数值病态问题。边界位移沿厚度方向非线性分布的假设可以适当减少数值结果收敛要求的薄层数。数值结果可作为其它数值方法或半解析法的标准解。     

压电驱动器非线性机电耦合动力学求解与验证

基于压电非线性效应和位移非线性效应建立了压电驱动器非线性机电耦合动力学方程,应用Linz  Ted-Poincaré法对弱非线性自由振动、接近共振时受迫振动及亚谐波振动响应方程进行推导,比较了压电驱动器在非线性及线性条件下响应的区别,使用四阶Runge-Kutta数值法和实验对理论推导进行了验证。结果表明:在两种非线性效应中,压电非线性对压电驱动器振动响应的影响是主要的;非线性数值解与解析解吻合较好,实验频率更接近非线性共振频率。     

轧机主传动系统强非线性扭振研究

建立含非线性刚度的两自由度轧机主传动系统扭振模型,通过参数代换得到该系统的强非线性动力学方程。应用能量迭代法得出系统存在主振动和亚谐振动周期解的必要条件,并求解此二阶强非线性非自治系统的频响函数及解析近似解。以某厂3800轧机主传动系统为例,利用数值仿真研究了非线性刚度、线性阻尼、扰动力矩对系统主振动和1/3次亚谐振动幅频特性的影响规律。研究结果为分析此类含非线性刚度的轧机主传动系统扭振特性提供一定的理论指导和参考。     

压电谐波电机驱动系统非线性主共振分析

为了探索压电谐波电机的机械-压电系统的非线性共振特性,设计了一种集压电驱动、谐波传动和活齿传动为一体的机电集成压电谐波电机。在非线性压电和非线性弹性效应的基础上,建立了驱动系统非线性机电耦合动力学方程。利用Linz Ted-Poincaré法推导了驱动系统非线性主共振响应方程,得出了主共振幅频响应曲线,分析了不同非线性效应对主共振响应的影响,最后通过四阶Runge-Kutta数值法验证了解析解的正确性。结果表明:在两种非线性效应中,非线性压电效应对主共振响应的影响是主要的;压电堆主共振出现在偏离固有频率较远处,且随着频率改变响应值出现跳跃现象;数值解与解析解响应曲线吻合较好。     

非线性轴承-转子系统的稳定性和分岔

研究了非解析径向椭圆轴承支承的转子系统的稳定性和分岔。考虑了转动惯量的影响,利用非线性油膜力以增加数值计算的精度。在不需要额外再解Reynolds方程的情况下,采用等参有限元法,求解了具有Reynolds边值条件的流体润滑椭圆型变分约束方程,使得动力积分过程中所需非线性油膜力及其Jacobian矩阵能够同时计算完成并且具有足够且协调一致的精度。在稳定性分析中,运用打靶法和轨迹预测追踪算法研究了系统非线性不平衡响应,结合Floquet理论研究了随着轴承设计参数改变时非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。     

非线性吸收效应对自相似脉冲传输特性的影响

以描述光纤放大器中飞秒脉冲演化的高阶非线性薛定谔方程为理论模型,采用分步傅里叶方法,对非线性吸收效应及放大器系统中的自相似脉冲传输的特性及其影响,进行了数值模拟研究,结果表明:随着非线性饱和吸收效应参数绝对值变大,自相似脉冲的功率会逐渐减小,峰值振幅也变得越来越小,而脉冲宽度则呈现略微增大的变化趋势。     

A variationally based nonlocal damage model to predict diffuse microcracking evolution

We explore a variationally based nonlocal damage model, based on a combination of a nonlocal variable and a local damage variable. The model is physically motivated by the concept of “nonlocal” effective stress. The energy functional which depends on the displacement and the damage fields is given for a one-dimensional bar problem. The higher-order boundary conditions at the boundary of the elasto-damaged zone are rigorously derived. We show that the gradient damage models can be obtained as particular cases of such a formulation (as an asymptotic case). Some new analytical solutions will be presented for a simplified formulation where the stress–strain damage law is only expressed in a local way. These Continuum Damage Mechanics models are well suited for the tension behaviour of quasi-brittle materials, such as rock or concrete materials. It is theoretically shown that the damage zone evolves with the load level. This dependence of the localization zone to the loading parameter is a basic feature, which is generally well accepted, from an experimental point of view. The computation of the nonlocal inelastic problem is based on a numerical solution obtained from a nonlinear boundary value problem. The numerical treatment of the nonlinear nonlocal damage problem is investigated, with some specific attention devoted to the damageable interface tracking. A bending cantilever beam is also studied from the new variationally based nonlocal damage model. Wood’s paradox is solved with such a nonlocal damage formulation. Finally, an anisotropic nonlocal tensorial damage model with unilateral effect is also introduced from variational arguments, and numerically characterized in simple loading situations.     

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

This paper provides the static and dynamic pull-in behavior of nano-beams resting on the elastic foundation based on the nonlocal theory which is able to capture the size effects for structures in micron and sub-micron scales. For this purpose, the governing equation of motion and the boundary conditions are driven using a variational approach. This formulation includes the influences of fringing field and intermolecular forces such as Casimir and van der Waals forces. The differential quadrature (DQ) method is employed as a high-order approximation to discretize the governing nonlinear differential equation, yielding more accurate results with a considerably smaller number of grid points. In addition, a powerful analytical method called parameter expansion method (PEM) is utilized to compute the dynamic solution and frequency-amplitude relationship. It is illustrated that the first two terms in series expansions are sufficient to produce an acceptable solution of the mentioned structure. Finally, the effects of basic parameters on static and dynamic pull-in instability and natural frequency are studied.     

3-RPS并联平台机构的位置正解与奇异构形分析的数值-符号解

基于Groebner基法和计算机符号处理技术,对3-RSP并联平台机构的位置正解问题进行了符号求解。该法通过对变量排序、建立多项式对的集合、求SP多项式和约简等运算,将一组非线性方程组化简为等价的三角化方程组,得到了封闭形式的解析解。推导了雅可比矩阵和数字一符号表示的奇异位形判别的解析表达式,对该并联机构的可操作性和奇异性进行了分析。同时给出了具体数值实例。     

Higher order explicit solutions for nonlinear dynamic model of column buckling using variational approach and variational iteration algorithm-II

This paper deals with the determination of approximate solutions for a model of column buckling using two efficient and powerful methods called He’s variational approach and variational iteration algorithm-II. These methods are used to find analytical approximate solution of nonlinear dynamic equation of a model for the column buckling. First and second order approximate solutions of the equation of the system are achieved. To validate the solutions, the analytical results have been compared with those resulted from Runge-Kutta 4th order method. A good agreement of the approximate frequencies and periodic solutions with the numerical results and the exact solution shows that the present methods can be easily extended to other nonlinear oscillation problems in engineering. The accuracy and convenience of the proposed methods are also revealed in comparisons with the other solution techniques.     

Static analysis of nanobeams using nonlocal FEM

A very efficiently finite element model is developed for static analysis of nanobeams. Nonlocal differential equation of Eringen is exploited to reveal a scale effect of nanobeams through nonlocal Euler-Bernoulli beam theory. The equilibrium equation of nonlocal beam is derived based on the variational statement. The element stiffness matrix and force vector are presented. The novelty and accuracy of this model is presented and verified. It is found that, this model is more accurate than others and can consider as a benchmark. The effects of nonlocality, boundary conditions, and slenderness ratio are figured out. The deflection of multi-span nanobeam is also illustrated. The present model can be used for static analysis of single-walled carbon nanotubes. Complex geometry and nonlinear boundary conditions can also be included.     

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen’s equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis.     

Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by AGM

The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji’s method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.     

基于多孔介质模型的机械密封静压泄漏特性分析

针对接触式机械密封普遍存在的渗漏现象,考虑到流体在多孔介质中的流动和在密封端面间的流动具有相似特征,基于多孔介质模型建立密封端面间渗流模型,通过对动量方程和连续性方程的推导,得到适用于密封端面间流体流动的控制方程,提出一种密封端面间泄漏率的解析计算新方法,并与COMSOL数值模拟得到的泄漏率进行对比分析;研究孔隙率、端面表面粗糙度、膜厚、密封介质压力和弹簧比压对静压泄漏特性的影响规律。结果表明,泄漏率随孔隙率、端面表面粗糙度、膜厚和密封介质压力的增大而增大,随弹簧比压的增大而减小,解析计算结果和数值模拟结果的变化趋势基本一致,证明该解析法计算泄漏率具有实用性和可行性。     

用Lyapunov指数研究单对齿轮间隙非线性系统的动力学行为

在间隙函数为分段线性函数的单对齿轮系统非线性微分方程量纲一化的基础上，给出院 系统的精确解析解，直接从Lyapunov指数的定义出发，给出了计算最大Lyapunov指数的数值方法，作出了系统随激励频率变化时的Lyapunov指数图，并扰此判别了系统中所存在的周期和混沌吸引子，研究结果表明，Lyapunov指数确是判定齿轮系统非线性动力学状态的一种可靠的特征指标。     

悬臂梁裂纹参数的识别方法

以梁振动理论作为基础 ,将含裂纹梁的振动问题转化为由弹性铰联接两个弹性梁系统的振动问题 ,得到理论计算含裂纹梁振动频率的特征方程。由此特征方程计算得到裂纹深度参数和位置参数变化时悬臂梁振动固有频率的变化规律。利用计算裂纹悬臂梁振动固有频率的特征方程 ,提出一种辩识裂纹深度和位置参数的数值计算方法。并通过对模拟悬臂梁裂纹的分析说明文中方法的有效性。