完全与不完全叉形分岔

 介绍一种可演示完全与不完全叉形分岔的实验装置，并分析其机理. 希望对非线性 动力学实验设计有一定启示作用.     

二阶微分方程含有时变参数的非完全分岔的分析

用新方法研究二阶微分方程含有时变参数的非完全分岔问题。当分岔参数随时间线性慢变分别经过定常跨临界分岔值，叉型分岔值和鞍结分岔值时，分析了非完全分岔参数和时变参数的变化率对分岔转移迁的滞后和跃迁现象的影响，并给出分岔转迁发生的一般条件。通过数值计算给出分岔转迁区和分岔转迁值，还讨论了解对初值和参数的敏感性问题。     

不完全理想约束与用广义力表示的达朗贝尔原理

以广义理想约束力是否为零,把理想约束定义为完全理想约束或不完全理想约束,并遵循拉格朗日思想,把达朗贝尔原理改造成广义力形式．     

不完全理想约束与用广义力表示的达朗贝尔原理

以广义理想约束力是否为零,把理想约束定义为完全理想约束或不完全理想约束,并遵循拉格朗日思想,把达朗贝尔原理改造成广义力形式．     

基于混合反馈控制的分数阶混沌系统多延时完全同步

为提高保密通信的安全性,本文首次将完全同步和延时投影同步的思想相结合提出了多延时完全同步。针对Lorenz、金融分数阶两个不同的混沌系统,基于分数阶稳定性理论以及混合反馈控制方法,通过设计能够自动调节反馈增益系数的混合反馈控制器,实现了分数阶多延时完全同步。根据前人提出的修正的预估校正算法对混沌系统进行数值仿真,结果表明由驱动系统与响应系统构建的多延时完全同步误差系统将最终稳定于零点,从而验证了混合反馈控制器的有效性和可行性。     

一种分析摆盘发动机震动力完全平衡的新方法

从机构学角度出发,抽象出摆盘发动机的RRSSC空间机构模型,通过对连杆进行震动力等效简化,将摆盘机系统分为一个复合开式链结构和一个多活塞圆形结构,分别考虑它们的震动力完全平衡问题,结果说明,只需在主轴上附加一个平衡重即可达到整个系统的震动力完全平衡．这种平衡分析方法比按照单环RRSSC机构分析的平衡方法简单、实用,符合特定环境中的使用要求．     

非完全相关荷载下钢筋混凝土框架结构体系可靠度分析

目前框架结构体系可靠度分析大多是在荷载完全相关的假定下完成的,对于非完全相关荷载作用下的体系可靠度研究则鲜有涉及,对于非理想弹塑性或弹脆性的结构尤其如此.本文在随机系统分析的概率密度演化理论的基础上,结合结构非线性全过程分析的位移控制算法,推导了基于归一化位移参数的结构非线性发展概率密度演化方程和承载力裕度的概率密度演化方程.采用纤维梁柱单元进行非线性分析,研究了钢筋混凝土框架结构在非完全相关荷载下的体系可靠度,并与Monte Carlo法进行了对比分析,证明了文中建议方法的可行性.基于文中方法,分析了荷载相关性对可靠度的影响,计算结果表明,荷载相关性对体系可靠度有比较明显的影响.     

分数阶Chen混沌系统的完全同步与反相同步

以分数阶 Chen 系统为例,分析了该系统的混沌特性,并对其分别进行了完全同步与反相同步控制.首先,基于分数阶系统稳定性理论和非线性动力学理论,构造出相应的非线性控制器,由此实现了分数阶 Chen 混沌系统的完全同步与反相同步控制;其次,利用分数阶稳定性理论,对上述同步给出了严格的数学证明;最后,借助于 Adams-Bashforth-Moultom 算法,利用数值模拟验证了所提方法的有效性.     

不完全测量系统鲁棒SGQKF的传递对准滤波器设计和稳定性分析

针对复杂环境下运载体观测信息不完全测量并且存在随机干扰不确定的传递对准问题,研究了不完全测量随机不确定系统的鲁棒稀疏网格求积分(H_∞-SGQKF)的高斯逼近滤波算法。基于非线性离散系统的最优贝叶斯滤波框架和间断观测滤波算法以及不确定性扰动噪声下的H_∞范数的鲁棒SGQKF算法,给出了不完全测量的稀疏网格求积分的高斯逼近滤波算法;通过非线性系统随机稳定性理论,分析并给出了系统估计误差和估计误差方差有界的充分条件,同时给出了系统稳定的不完全测量时的丢包率临界值,证明间断观测条件下的不完全测量H_∞-SGQKF算法是稳定的。通过传递对准仿真试验和某型激光捷联式惯性导航系统的跑车试验对该算法进行了验证。结果表明,该方法比未采用鲁棒的不完全测量的稀疏网格求积分滤波的传递对准精度有所提高,说明不完全测量的鲁棒稀疏网格求积分滤波算法是正确的、稳定的,并且具有鲁棒性能。     

完全变换法在无网格伽辽金方法中的应用

由于移动最小二乘形函数一般不具有常规有限元或边界元形函数所具有的插值特征，本质边界条件的处理成为无网格伽辽金法实施中的一个难点。本文通过建立节点位移和广义位移之间的关系对移动最小二乘形函数进行修正，给出了修正的移动最小二乘形函数；以二维问题为例，对完全交换法在无网格伽辽金方法中的应用进行了研究，实现了本质边界条件在节点处的精确施加。数值计算结果表明该方法不仅简单合理，而且具有较高的精度、收敛性和稳定性。     

Periodic Delay Effects on Cutting Dynamics

We consider a delay equation whose delay is perturbed by a small periodic fluctuation. In particular, it is assumed that the delay equation exhibits a Hopf bifurcation when its delay is unperturbed. The periodically perturbed system exhibits more delicate bifurcations than a Hopf bifurcation. We show that these bifurcations are well explained by the Bogdanov-Takens bifurcation when the ratio between the frequencies of the periodic solution of the unperturbed system (Hopf bifurcation) and the external periodic perturbation is 1:2. Our analysis is based on center manifold reduction theory.     

多种非线性力作用下不平衡弹性转子的分岔特性

研究了4自由度不平衡弹性转子在非线性油膜力、非线性内阻力和非线性弹性力联合作用下的动力学特性。结果表明，当只有非线性油膜力作用时，转子只存在由于油膜失稳而导致的倍周期分岔。而当非线性油膜力与非线性内阻力共同作用时，在油膜失稳后，转子产生低频振动。转速继续增加，还会诱发内阻失稳，产生概周期运动。在倍周期分岔中，存在分岔激变现象。本文发现的由于油膜涡动而导致的内阻失稳(概周期运动)是一种未见报道的转子失稳模式(组合失稳)，它与油膜失稳(倍周期运动)一起可作为转子故障诊断的典型失稳模式。     

Solution of the connection problems between a finite holed plate and a stiffener by using the partitioning concept of the generalized variational method

In this paper a new finite element method is presented, in which complex functions are chosen to be the finite element model and the partitioning concept of the generalized variational method is utilized. The stress concentration factors for a finite holed plate welded by a stiffener are calculated and the analytical solutions in series form are obtained. From some computer trials it is demonstrated that the problem of displacement compatibility and continuity of tractions between the holed plate and the stiffener is successfully analysed by using this method. Since only three elements need to be formulated, relatively less storage is required than the usual finite element methods. Furthermore, the accuracy of solutions is improved and the computer time requirements are considerably reduced. Numerical results of stress concentration factors and stresses along the welded-line which may be referential to engineers are shown in tables.     

Experiments on the Onset of Impacting Motion Using a Pipe Conveying Fluid

The transition from stable periodic nonimpacting motion to impacting motion, due to variations of parameters, is observable in a wide range of vibro-impact systems. Recent theoretical studies suggest a possible scenario for this type of transition. A key element in the proposed scenario is fulfilled if the oscillatory motion involved in the transition is born in a supercritical Hopf bifurcation. If the onset of impacting motion is close to the Hopf bifurcation, the impacting motion is likely to be chaotic. A numerical simulation of a system of articulated pipes conveying fluid is used to illuminate the theory. An experimental setup is presented, where a cantilevered pipe conveying fluid is unilaterally constrained. Results from experiments are found to be in good qualitative agreement with the theory.     

Nonlinear dynamics of hardware-in-the-loop experiments on stick–slip phenomena

A single degree-of-freedom nonlinear mechanical model of the stick–slip phenomenon is studied when the Stribeck-type friction force is emulated by means of a digitally controlled actuator. The relative velocity of the slipping contact surfaces is considered as bifurcation parameter. The original physical system presents subcritical Hopf bifurcation with a wide bistable parameter region where stick–slip and steady-state slipping are both stable locally. Hardware-in-the-loop experiments are performed with a physical oscillatory system subjected to the emulated Stribeck forces. The effect of sampling time is studied with respect to the stability and nonlinear behavior of this experimental system. The existence of subcritical Neimark–Sacker bifurcations are proven in the digital system, the stability and bifurcation characteristics of the continuous and the digital systems are compared, and the counter-intuitive stabilizing effect of sampling time is shown both analytically and experimentally. The conclusions draw the attention to the limitations of hardware-in-the-loop experiments when the corresponding systems are strongly nonlinear.     

A STUDY OF THE CATASTROPHE AND THE CAVITATION FOR A SPHERICAL CAVITY IN HOOKE’S MATERIAL WITH 1/2 POISSON’S RATIO

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Codimension two bifurcation of a vibro-bounce system

A three-degree-of-freedom vibro-bounce system is considered. The disturbed map of period one single-impact motion is derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. Dynamical behavior of the system, near the point of codimension two bifurcation, is investigated by using qualitative analysis and numerical simulation. It is found that near the point of Hopf-flip bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. The results from simulation show that there exists an interesting torus doubling bifurcation near the codimension two bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transform to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems. Different routes from period one single-impact motion to chaos are observed by numerical simulation.The project supported by the National Natural Science Foundation of China (10172042, 50475109) and the Natural Science Foundation of Gansu Province Government of China (ZS-031-A25-007-Z (key item))     

ROBUST CONTROL OF PERIODIC BIFURCATION SOLUTIONS

The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method. According to obtained bifurcation diagrams and combining control theory, the method of robust control of periodic bifurcation was presented, which differs from generic methods of bifurcation control. It can make the existing motion pattern into the goal motion pattern. Because the method does not make strict requirement about parametric values of the controller, it is convenient to design and make it. Numerical simulations verify validity of the method.     

Classification of parametrically constrained bifurcations

If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.     

Higher-order Melnikov method

In this paper the Melnikov method has been generalized to the case of higher-order byfinding an explicit expression for second-order subharmonic Melnikov function,and it hasbeen proved that the existence of subharmonic or hyper-subharmonic of a system can beproved under certain conditions by use of second-order Melnikov function.