变流速输液管的周期和混沌振动

研究了参数激励和外激励联合作用下输流管道的非线性振动问题．只考虑管道变形的几何非线性因素,利用Hamilton原理得到单侧受简谐均布载荷作用下输液管的非线性动力学方程,对系统运动偏微分方程综合运用多尺度法和Galerkin离散方法,得到了主参数共振-1／2亚谐共振和1：2内共振情况下的平均方程．数值模拟结果表明参数激励和外激励联合作用下的悬臂输液管呈现周期运动、多倍周期运动和混沌运动的变化规律．     

受电压激励的复合材料悬臂板的分叉分析

以飞行器机翼作为工程背景,将机翼简化为悬臂板模型,研究了受横向电压激励、基础激励、面内激励联合作用下复合材料层合悬臂板的非线性动力学问题.首先建立其动力学模型,考虑冯-卡门大变形理论,利用Hamilton原理建立复合材料层合悬臂板的非线性动力学方程;选择符合边界条件的模态函数,利用Galerkin方法对系统进行四阶离散,得到四自由度非线性常微分方程;代入系统实际物理参数,应用MATLAB软件数值模拟得到系统振动幅值随电压激励变化的分叉图,由图可知,电压激励使系统从混沌运动变为倍周期运动,降低了系统振幅,保持系统的稳定.     

两点碰撞振动系统的周期运动与分叉

建立了两自由度两点碰撞振动系统的动力学模型,给出了碰撞振动系统产生粘滞的条件,分析了系统存在的粘滞运动.采用打靶法,利用变步长逐次迭代逼近的方法求解系统的不稳定的周期碰撞运动,即Poincar啨截面上的不动点.通过对两自由度两点碰撞振动系统进行数值模拟显示了系统在一定参数条件下存在周期倍化分叉和Hopf分叉,同时通过数值模拟的方法得到了以两自由度两点碰撞振动系统Poincar啨截面上的不变圈表示的拟周期响应,并进一步分析了随着分岔参数的变化,两自由度两点碰撞振动系统周期运动经拟周期分叉和周期倍化分叉向混沌的演化路径.     

基于最大Lyapunov指数的行星齿轮传动系统混沌特性分析

为了分析行星齿轮系统的混沌特性,基于集中参数理论,考虑时变啮合刚度、齿隙和综合啮合误差等非线性因素,建立行星齿轮系统扭转振动模型.采用Runge-Kutta数值解法求解振动方程,利用分岔图和最大Lyapunov指数图分析系统随各种参数变化的分岔与混沌特性.数值仿真得出:随激励频率的增加,系统首先从周期运动进入阵发性混沌,再通过逆倍化分岔由混沌回到周期运动,之后再次通过跳跃激变和倍化分岔由周期运动进入混沌运动,最后通过逆倍化分岔稳定到1周期运动.随阻尼比的增加,系统通过逆倍化分岔由混沌运动进入周期运动.随综合啮合误差幅值、齿隙和刚度幅值分别增加的三种情况下,系统都是通过倍化分岔由周期运动进入混沌运动.随荷载的增加,系统通过跳跃激变和逆倍化分岔由混沌运动进入周期运动.以上分析结果可为行星齿轮系统参数设计提供理论依据.     

复合材料层合板的双Hopf分叉分析

利用高维非线性系统的Hopf分叉定理,研究复合材料层合板的双Hopf分叉.研究了一类受面内激励和横向外激励联合作用下的复合材料层合板在主参数共振—1∶1内共振情况下的双Hopf分叉.首先利用多尺度法得到系统的平均方程,经过简化得到了系统的分叉响应方程.根据对分叉响应方程的分析,得到了系统平衡解的稳定性临界曲线,并给出了系统产生双Hopf分叉的条件.利用数值方法得到系统在参数平面上的分叉集,通过对不同分叉区域的分析,我们发现随着参数的变化复合材料层合板存在不同的周期运动现象.     

不同脱层位置下脱层屈曲梁振动实验研究

通过实验对一端固定一端夹支脱层屈曲梁在轴向周期激励作用下的非线性动力响应进行了实验研究.利用位移时间历程图,相图和频谱图,对多组不同脱层位置下脱层屈曲梁的非线性动力响应进行了分析.实验表明脱层梁结构存在倍周期以及混沌运动等非线性动力学行为.同时实验还表明,在相同的脱层长度下,脱层位置对脱层梁的动力学特性有明显影响,即脱层区域中心越靠近梁结构的中心位置,脱层梁的一阶自然频率越低,且越容易在较低的激励频率和激励荷载下发生周期分叉和混沌等行为.     

弱非线性耦合二维各向异性谐振子的动力学行为

研究了弱非线性耦合二维各向异性谐振子的奇点稳定性及其在相空间中的轨迹.首先,求得弱非线性耦合二维各向异性谐振子的奇点;其次,分别利用Lyapunov间接法和梯度系统方法讨论该系统的平衡点稳定性;最后,用Matlab方法对系统进行数值模拟,并运用庞加赖截面观察系统在相空间的运动轨迹,发现随着能量的增加系统经历规则运动、规则运动与混沌并存等阶段,最后出现了混沌现象.     

Host-Parasitoid系统的分岔与混沌控制

用数值模拟的方法,研究了Host-Parasitoid模型.该模型是一类非线性离散系统,反映了在一定的时间和空间内,寄生虫和寄宿主之间的生存状态.通过调节各种影响下的分岔参数,可以观察到系统具有周期泡,倍周期分叉,间歇混沌和Hopf分岔等复杂非线性动力学现象,揭示了系统通向混沌的途径.利用不同周期遍历下的奇怪吸引子和具有分形边界的吸引盆对系统的非线性特性进行了深入的探讨.最后利用参数开闭环控制法对系统的混沌状态进行了有效的控制.数值仿真和理论分析表明,选择相应的控制参数可将该系统的混沌状态控制到不同的稳定周期运动.     

压电纤维复合材料层合壳的非线性动力学研究

本文对横向激励作用下的1-3型压电纤维复合材料层合壳进行了非线性动力学分析,并研究了压电特性对结构振动响应的影响.首先建立了压电纤维复合材料层合壳的非线性动力学方程,并且在已知的几何结构和材料特性基础上考虑了电场属性.然后根据位移边界条件,选择合适的振型函数,通过Galerkin方法将运动控制方程转化成两自由度的非线性常微分方程.通过数值模拟方法分析了横向激励和压电系数对压电纤维复合材料层合壳非线性振动特性的影响.通过波形图、三维相图、庞加莱图和分叉图等来研究壳体不同类型的周期和混沌运动.结果表明,外激励作用下结构存在复杂的非线性振动响应,同时压电参数对层合壳结构振动响应具有很强的调节作用.     

参数激励和外激励联合作用下薄板的非线性动力学

研究了在参数激励和外激励联合作用下四边简支矩形薄板的非线性动力学.基于von Karman理论,推导出了在参数激励和外激励联合作用下四边简支矩形薄板的动力学方程.利用Galerkin法对偏微分方程进行三阶离散,得到一个三自由度的常微分方程.考虑1:2:4内共振-主参数共振-1/2亚谐共振的情况,利用多尺度法得到了薄板系统的六维的平均方程.最后,采用数值方法研究了薄板的周期和混沌运动.结果发现外激励对薄板的混沌运动是敏感的.     

粘弹性传动带的分岔特性和混沌振动分析

研究了粘弹性传动带横向振动的分岔特性和混沌动力学行为．将传动带视为沿轴向运动的抗弯刚度较 小的粘弹性梁模型,同时考虑变形的几何非线性和材料的非线性因素,运用弹性力学方法建立了其横向振动 的偏微分方程,利用 Galerkin 方法得到了时空坐标解耦的二阶非线性动力学方程,重点探讨了带速波动对系统 动态特性的影响．采用数值方法对系统的运动响应进行仿真,分岔图和 Poincaré图表明：随着平均带速和波动 幅值的变化,系统出现周期振动和混沌振动,倍周期分岔是产生混沌振动的途径．     

梁摆系统耦合振动分析

分析了梁摆系统的耦合振动,梁和摆均考虑为线性.研究发现该系统含有非线性动力行为,在某些条件下会发生叉形分叉.用结构动力学理论建立了梁摆系统的耦合振动方程,用摄动法求出了系统的近似解,分析了该系统的动力响应及分叉.最后用MATHMATIC软件对分叉点前后动力响应进行分析.     

Bifurcations and chaotic motions of a curved pipe conveying fluid with nonlinear constraints

This paper investigates the bifurcations and chaotic motions of a fluid-conveying curved pipe restrained with nonlinear constraints. The nonlinear equation of motion for the curved pipe is derived by forces equilibrium on microelement of the system under consideration. Depending on the nonlinear equation of motion and the corresponding boundary conditions for the curved pipe, the DQM (differential quadrature method) is introduced to formulate the discrete forms of the equation of motion for the system, which is then solved by numerical methods. Calculations of phase-plane portraits, time history diagrams, PS (Power Spectrum) diagrams, bifurcation diagrams and Poincaré maps of the oscillations establish clearly the existence of the chaotic motions. In addition, the result shows the route to chaos for the pipe is via period-doubling bifurcations, which is affected definitively by several parameters of the system.     

Helicoseir as Shape of a Rotating String (II): 3D Theory and Simulation Using ANCF

This paper is the second one devoted to studying the dynamical behavior of a rotating uniform string with one fixed top point. Two-dimensional shapes of relative equilibrium for a string were analyzed in our paper [3] both analytically and numerically and found to be instable. This fact disagrees with the experimental appearance of this so-called helicoseir problem because one can easily demonstrate that its stable motion is possible. In this paper, spatial nonlinear equations of motion are derived and shown that a 2D equilibrium equation is one of their partial cases. The equations are, however, very complicated that is why we decided at first to analyze the motion numerically by a finite element approach called the absolute nodal coordinate formulation (ANCF). We developed a new 12-dof element of a thin string based on the Euler-Bernoulli theory. The simulation shows that the undamped spatial motion of the helicoseir is stable and looks like self-excited oscillations near the flat instable configurations that were obtained previously. This stability is destroyed when external damping is added to the system. Some examples of bifurcation instability fore spatial motion are presented; they satisfy the bifurcation diagram obtained in the previous work. Unfortunately, numerical simulation cannot give answers to some interesting questions, e.g. dependence of parameters of the self-excited oscillations on the angular velocity of rotation. Thus, further analytical research of this problem is desirable.     

一个新的多翅膀混沌系统分析与同步

提出了一个新的三维自治混沌系统,通过分析系统的李亚普诺夫指数谱和分岔图可得新系统具有如下性质： 双恒李亚普诺夫指数谱混沌锁定,锁定后的混沌系统的幅值和相位可调节．根据该混沌系统的平衡点和吸引子的拓扑结构,通过构造偶对称多分段平方函数族,可实现在某一方向上扩展指标2的鞍焦平衡点,从而实现多翅膀的扩展．设计了混沌电路实现,验证了电路实现与仿真结果的一致性．最后针对扩展后的多翅膀混沌系统,通过选取合适的驱动信号,达到响应系统与驱动系统混沌同步,并通过仿真验证了所得的结果．     

Nonlinear Feedback Control for the Lorenz System

The Lorenz system is well known for its ability to produce chaotic motion and the control problem of this system has attracted much attention in recent years. In this paper, control of the Lorenz chaotic systems based on a nonlinear feedback technique is presented. The objective of control is two-fold: one is to drive the system to one of equilibrium points associated with uncontrolled chaotic motion and the other is to let one of the closed-loop system states track a given signal. The controllers designed here are based on exact linearization theory of nonlinear systems and can regulate the closed-loop system states globally to a given point. Finally, illustrative examples show the effectiveness of the proposed design method.     

Synchronization of chaotic attractors with different equilibrium points

This paper investigates the synchronization of coupled chaotic systems with many equilibrium points. By addition of an external switching piecewise-constant controller, the system changes to a new one with several independent chaotic attractors in the state space. Then, by addition of a nonlinear state feedback control, the chaos synchronization is presented. This method can be used in many couples of chaotic systems characterized by the same equilibrium point or by two different equilibrium points, even they are the same systems (Lorenz, Jerk, Van der Pol) or two chaotic systems with different structures (Lorenz modified).     

An Exponential Chaotic Oscillator Design and Its Dynamic Analysis

After years of development, chaotic circuits have possessed many different mathematic forms and multiple realization methods. However, in most of the existing chaotic systems, the nonlinear units are composed of the product terms. In this paper, in order to obtain a chaotic oscillator with higher nonlinearity and complexity to meet the needs of utilization, we discuss a novel chaotic system whose nonlinear term is realized by an exponential term. The new exponential chaotic oscillator is constructed by adding an exponential term to the classical Lü system. To further investigate the dynamic characteristics of the oscillator, classical theoretical analyses have been performed, such as phase diagrams, equilibrium points, stabilities of the system, Poincaré mappings, Lyapunov exponent spectrums, and bifurcation diagrams. Then through the National Institute of Standards and Technology (NIST) statistical test, it is proved that the chaotic sequence generated by the exponential chaotic oscillator is more random than that produced by the Lü system. In order to further verify the practicability of this chaotic oscillator, by applying the improved modular design method, the system equivalent circuit has been realized and proved by the Multisim simulation. The theoretical analysis and the Multisim simulation results are in good agreement.      

随机激励作用下船舶横摇运动的奇异非混沌动力学

基于一类规则横浪作用下的单自由度船舶横摇运动模型,考虑恢复力矩和阻尼力矩的非线性因素,以一低干舷船模为例,利用龙格库塔法求解了横摇运动方程,通过时间庞加莱截面绘制了系统的分岔图;考虑其受随机风荷载扰动下不同周期吸引子演变成奇异非混沌吸引子的具体过程,发现周期激励系统在随机激励扰动下同样存在奇异非混沌吸引子,且当分岔参数离混沌区域越远,所需要随机激励的幅值越大才能诱发奇异非混沌吸引子.通过最大李雅普诺夫指数验证吸引子的非混沌性;采用奇异连续谱和分形图刻画吸引子的奇异性.