论三维非线性断裂动力学中的路径无关积分

本文讨论三维非线性断裂动力学中的路径无关积分,它是文[4]关于二维情况结果的拓充.在研究三维非线性固体中埋藏裂纹或表面裂纹的动力传播问题中,这种拓充是必要的.固体介质是非线性弹性的或弹塑性的的情况均被加以考虑,并作出了相应的向量型路径无关积分.解释了这种路径无关积分的力学意义,它被证明联系于动力裂纹扩展力,因而,它们可用于构作非线性断裂动力学中的断裂准则.     

新三维非线性系统的动力学分析

通过代数方法,构造出来一个具有复杂混沌吸引子的非线性混沌自治三维系统．从理论和数值两方面对吸引子进行了分析和仿真,得到了系统在平衡点处不稳定的参数范围．通过分岔图和Lyapunov指数谱进一步揭示了系统丰富的动力学行为.     

六维系统环形桁架天线的非线性动力学分析

随着科技的发展,大尺度、低重量、易收拢、高精度等特点是未来天线的主要发展方向.环形桁架天线在发射时整体处于收拢状态,升空后按指令有顺序展开,节省了航天器的空间.此外,环形桁架天线可根据需求设计展开口径的大小.所以,环形桁架天线是目前较为理想的天线结构形式.由于自身结构特点以及复杂的空间环境因素,天线在运行时易产生大幅度的非线性振动,严重影响卫星的稳定运行.因此,将环形桁架天线简化成等效圆柱壳模型,并建立其动力学方程.采用理论分析和数值模拟研究了六维系统环形桁架天线的非线性动力学特性.利用规范型理论化简系统方程分析未扰系统和扰动系统的非线性动力学行为,利用能量相位法验证环形桁架天线系统具有Shilnikov型多脉冲混沌运动,利用数值模拟验证理论分析.并通过数值模拟研究了热激励对环形桁架天线系统非线性振动的影响.     

Nonlinear Vibration of a Pendulum in a Viscous Stream

Zusammenfassung In dieser Arbeit wird eine Regelgleichung, die den Gang eines Stabpendels in einem Reibungsstrom von veränderlicher Geschwindigkeit beschreibt, entwickelt. Nichtlineare Effekte, die durch Reibungskräfte verursacht sind, und grosse Stabamplituden sind in der Diskussion eingeschlossen. Wir setzen voraus, dass die Reibungskräfte sowohl am Stab als auch am eigentlichen Pendelkörper wirken. Die Methode erster Ordnung von Krylov und Bogoliuboff ergibt eine approximative allgemeine Lösung der Bewegungsgleichung. Wir wenden die Lösung auf den Spezialfall eines Pendels in einem gleichmässigen Reibungsstrom an.     

基于滑模方法的倒立摆台车系统的非线性控制

以倒立摆台车系统为研究对象，将系统状态分成两组，构造出一种双层滑动面，给出一种基于滑模控制的非线性控制律，并设计了控制器参数．然后采用Lyapunov方法，证明了各级滑动平面的稳定性，实现了台车在水平方向位置及摆角的渐近跟踪．     

Monitoring of the Nonlinear Dynamics of Railway Wheelsets

This paper focuses on the identification of dominant coherent structures in the nonlinear dynamic behavior of railway wheelsets by Karhunen-Loève-Transform (KLT). The ultimate goal is the characterization of the rolling quality of railway wheelsets. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

新三维自治混沌系统动力学性质研究

采用动力系统理论分析和计算机数值仿真相结合的方法,研究了一类新三维自治混沌系统的非线性动力学行为,如平衡点及其稳定性、不变集、混沌吸引子、吸引域等,从而展示了该混沌系统的丰富的动力学特性并且用matlab给出了相应的计算机模拟.创新点在于同时考虑了该混沌系统的最终界和全局吸引集,并且对于这个混沌系统的任意正参数,分别得到了该混沌系统最终界的一个参数族数学表达式和全局指数吸引集的一个参数族数学表达式,最后利用交集的思想分别得到了混沌系统最终界和全局吸引集的一个较小的数学表达式.混沌系统有望在实际保密通信中得到应用.     

转子动力学的非线性数值求解

将Euler(欧拉)角表示引入转子动力学系统,用以描述转子的非线性旋转运动,并与时间有限元相结合,进而提出了包含非线性因素的转子动力学保辛数值求解方法.以此方法为基础,分析了悬臂梁-圆盘转子系统的涡动行为.数值结果证明该数值解法的有效性与正确性,可用于各种转子系统涡动行为分析.     

Dynamics of Semi-Discretizations of the Defocusing Nonlinear Schrodinger Equation

It has been demonstrated that the nonlinear Schrödinger(NLS) equation is sensitive to discretizations. In the focusingcase this is due to the homoclinic structure associated withthe NLS equation. In this paper we show that various numericalschemes for the defocusing case are also prone to instabilities,although not as severe as those of the focusing equation. Anintegrable discretization due to Ablowitz and Ladik does notsuffer from the same instabilities. However, it is shown thatit develops a focusing singularity if a threshold conditionis exceeded. Numerical examples illustrating the phenomena pertainingto the defocusing equation are given.     

Nonlinear Dynamics of Pipes with Pulsatile Flow

The dynamic behaviour of pipes conveying flowing fluid can be significantly influenced by the periodically changing flow. The fluid is considered to be incompressible, frictionless and its velocity relative to the pipe is harmonic function of time of which magnitude does not depend on spatial coordinates. The pipe is modelled as an inextensible continuum. The investigations were performed using three bifurcation parameters: the frequency, the perturbation amplitude and the mean flow velocity. In super‐critical case the nonlinear dynamics was shown in bifurcation diagrams.     

Global Regularity to the 3D Generalized MHD Equations with Nonlinear Damping Terms

In this paper, we consider the Cauchy problem of the 3D generalized MHD system with nonlinear damping terms. We establish the global existence of strong solutions with the help of damping terms. Furthermore, we consider the balance between damping terms.     

非线性弹性杆的异常动态响应

讨论了拉伸速度呈周期变化的受拉非线性弹性直杆的动力行为。采用Melnikov方法研究时发现,材料的非线性使得动力响应发生异常,对确定的直杆而言,当拉伸速度超过某个临界值时,动力系统将出现次谐分岔和混沌。     

Nonlinear Dynamics Equation in p-Adic String Theory

We investigate nonlinear pseudodifferential equations with infinitely many derivatives. These are equations of a new class, and they originally appeared in p-adic string theory. Their investigation is of interest in mathematical physics and its applications, in particular, in string theory and cosmology. We undertake a systematic mathematical investigation of the properties of these equations and prove the main uniqueness theorem for the solution in an algebra of generalized functions. We discuss boundary problems for bounded solutions and prove the existence theorem for spatially homogeneous solutions for odd p. For even p, we prove the absence of a continuous nonnegative solution interpolating between two vacuums and indicate the possible existence of discontinuous solutions. We also consider the multidimensional equation and discuss soliton and q-brane solutions.     

Dynamics of Nonlinear Random Walks on Complex Networks

Journal of Nonlinear Science - In this paper, we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition...     

Nonlinear Dynamics of Marine Systems in Random Waves

The dynamics of ships or offshore structures is influenced by several different effects, some of which have a distinctly nonlinear characteristic. Even though in many situations the motion can sufficiently be described by linear models, nonlinear phenomena play a crucial role in the investigation of some more critical operating conditions: Large amplitude motions, sudden jumps in the dynamical behavior and sensitivity to the initial conditions are likely to occur under some circumstances. The response of floating systems such as moored buoys and barges in regular waves can be approximated by analytical or numerical techniques. These analyses reveal the characteristics of different periodic motions. In order to determine how these responses change under a more general forcing, the motion of floating structures under the influence of random disturbances is described by probability distributions. Different mathematical tools can efficiently be applied to models with few degrees of freedom. The localized statistical linearization used here is also promising for larger systems. Modelling aspects of offshore structures and random waves are discussed as well as the determination of probability distributions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)