多频激励下Duffing vanderPol系统的两参数分岔分析

研究了含有两个分岔参数的多频激励下Duffing-van der Pol系统的分岔特性．分3种情况进行了讨论:情形1 将λ1看成分岔参数;情形2 将λ2看成分岔参数;情形3)将λ1和λ2都看成分岔参数．根据转迁集的定义,不同的情况下,整个参数空间都被分成了若干个不同的区域,得到了各个参数空间上系统的分岔图,从而为该类系统的参数优化控制奠定了基础．     

一类弹性储液箱同液体耦合晃动问题的分岔行为分析

建立了弹性圆柱型储液箱同液体耦合系统在外激励下的非线性振动方程组．采用多尺度法、奇异性理论研究此非线性振动系统共振解的分岔行为,通过对其分岔行为的分析和讨论,得到了这一系统的多种转迁集和分岔图,建立了系统参数与其拓扑分岔解的联系,并且分析了不同参数下系统的分岔特性,为实现储液器参数的优化控制提供了理论依据．     

非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究

研究了二元机翼非线性颤振系统的Hopf分岔．应用中心流形定理将系统降维,并利用复数正规形方法得到了以气流速度为分岔参数的分岔方程．研究发现,分岔方程中一个系数不含分岔参数的一次幂,故使得分岔具有超临界和亚临界双重性质．用等效线性化法和增量谐波平衡法验证了所得结果．     

一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究

研究了一类不可压的广义neo-Hookean材料组成的球体的空穴分岔问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压的neo-Hookean材料,得到了球体内部空穴生成的条件．与均匀各向同性的neo-Hookean球体的情况相比,证明了当摄动参数属于某些区域时,从平凡解局部向左分岔的空穴分岔解上存在一个二次转向分岔点,空穴生成时的临界载荷会比无摄动的材料的临界载荷小．用奇点理论证明了,空穴分岔方程在临界点附近等价于具有单边约束条件的正规形．用最小势能原理分别讨论了空穴分岔解的稳定性和实际稳定的平衡状态．     

弹性支承-刚性转子系统同步全周碰摩的分岔响应

基于航空发动机转子系统的结构特点,将航空发动机转子系统简化为一个非线性弹性支承的刚性转子系统．根据Lagrange方程建立了弹性支承-刚性不对称转子系统同步全周碰摩的运动方程;采用平均法进行求解,得到了关于系统振幅的分岔方程;根据两状态变量约束分岔理论,分别给出了系统在无碰摩和碰摩阶段参数平面的转迁集和分岔图,讨论了转子偏心、阻尼对系统分岔行为的影响;应用Liapunov稳定性理论分析了系统碰摩周期解的稳定性和失稳方式,给出了系统参数——转速平面上周期解的稳定范围;该文的研究结果对航空发动机转子系统的设计有一定的理论意义．     

具有平方、立方非线性项的耦合动力学系统1：2内共振分贫

对一类具有平方,立方非线性项的耦合动力学系统1：2内共振情形进行了研究,首先,用直接方法求出该系统1：2内共振时的Normal Form,该系统的Normal Form中,不仅含有平方非线性项,同时还含有立方非线性项,通过采用适当的变量变换,将4维分贫方程约化成3维,进而得到单变量4次分岔方程,最后用奇异性理论,研究了一类普适开折的分岔特性,该方法可用于4维中心流形上流的强内共振时的分岔行为分析。     

1∶1内共振悬索的二维奇异性分析

对1∶1内共振悬索系统的二维分岔方程进行了研究．根据奇异性理论得到了3种情况下开折系统的转迁集．转迁集将整个参数空间分成了不同的保持域,得到了各个保持域上的分岔图．     

具有平方、立方非线性项的耦合动力学系统1∶2内共振分岔

对一类具有平方、立方非线性项的耦合动力学系统1∶2内共振情形进行了研究A *D2首先,用直接方法求出该系统1∶2内共振时的Normal Form,该系统的Normal Form中,不仅含有平方非线性项,同时还含有立方非线性项A *D2通过采用适当的变量变换,将4维分岔方程约化成3维,进而得到单变量4次分岔方程A *D2最后用奇异性理论,研究了一类普适开折的分岔特性A *D2该方法可用于4维中心流形上流的强内共振时的分岔行为分析A *D2     

非线性转子-密封系统1∶2亚谐共振分岔研究

研究了转子-密封系统在气流激振力作用下的低频振动——1∶2亚谐共振现象．利用流体计算动力学（CFD）方法对转子-密封系统进行了流场模拟计算,辨识出适用于气流流场的Muszynska模型参数,并建立了转子-密封系统动力学方程．采用多尺度方法将系统进行3次截断,并得到系统响应．采用奇异性理论研究了系统的1∶2亚谐共振,进一步得到系统亚谐共振的分岔方程和转迁集,根据转迁集给出了在不同奇异性参数空间内的分岔图．同时,由分岔方程得到了亚谐共振非零解存在的条件．其分析结果对抑制转子-密封系统的亚谐振动有重要的工程意义．     

一类双面碰撞振子的对称性尖点分岔与混沌

讨论了一类单自由度双面碰撞振子的对称型周期n-2运动以及非对称型周期n-2运动．把映射不动点的分岔理论运用到该模型,并通过分析对称系统的Poincaré映射的对称性,证明了对称型周期运动只能发生音叉分岔．数值模拟表明:对称系统的对称型周期n-2运动,首先由一条对称周期轨道通过音叉分岔形成具有相同稳定性的两条反对称的周期轨道;随着参数的持续变化,两条反对称的周期轨道经历两个同步的周期倍化序列各自生成一个反对称的混沌吸引子．如果对称系统演变为非对称系统,非对称型周期n-2运动的分岔过程可用一个两参数开折的尖点分岔描述,音叉分岔将会演变为一支没有分岔的分支以及另外一个鞍结分岔的分支．     

解分数阶微分代数系统的Adomian分解方法

研究了利用Adomian分解求解分数阶微分代数系统的方法.分析了代数约束对Adomian方法求解的影响,指出直接解出代数约束变量,将原系统转化为微分系统进行Adomian分解的困难.提出确定代数变量级数解各分量的新方法,据此进行Adomian分解,得到整个系统的级数解.特别研究了代数约束为线性的分数阶微分代数系统的Adomian解法,证明了各变量间的线性代数约束关系可以转化为相应级数解中各分量的线性关系,从而方便求解,并结合具体例子证明了该方法简便有效.     

事件空间中单面非Chetaev型非完整系统的Noether定理

研究事件空间中单面非Ｃｈｅｔａｅｖ型非完整系统的Ｎｏｅｔｈｅｒ定理,首先给出了系统的Ｄ’Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理;其次基于该原理在无限小变换下的不变性,研究了非Ｃｈｅｔａｅｖ型非完整系统的Ｎｏｅｔｈｅｒ定理及逆定理;最后举例说明结果的应用。     

求解非定常非完整约束多体系统动力学的一种方法

通过对约束矩阵进行奇异值分解,将系统的动力学方程沿与约束相容和不相容的两个方向上投影,求解受非定常非完整约束的多体系统动力学问题,并给出了求约束反力的公式和避免违约的一种方法;这种解法不仅不依赖于描述系统的坐标选择,而且计算效率高。最后举了一个说明性例子。     

单面约束力学系统的Noether理论

应用就换群Ｃｒ的无限小群变换的广义准对称性，给出了受单面约束的动力学系统的Ｎｏｅｔｈｅｒ理论，并举例说明结果的应用。     

非Chetaev型非完整系统的Lie对称性与Noether对称性

研究非Ｃｈｅｔａｅｖ型非完整系统的Ｌｉｅ对称性与Ｎｏｅｔｈｅｒ对称性,具体研究了非Ｃｈｅｔａｅｖ型常 质量非完整系统和非Ｃｈｅｔａｅｖ型变质量非完整系统的Ｌｉｅ对称性与Ｎｏｅｔｈｅｒ对称性．给出Ｌｉｅ对称 性导致Ｎｏｅｔｈｅｒ对称性以及Ｎｏｅｔｈｅｒ对称性导致Ｌｉｅ对称性的条件．     

Hybrid inclusion and disclusion systems with applications to equilibria and parametric optimization

In this paper, we first establish the existence theorems of the solution of hybrid inclusion and disclusion systems, from which we study mixed types of systems of generalized quasivariational inclusion and disclusion problems and systems of generalized vector quasiequilibrium problems. Some applications of existence theorems to feasible points for various mathematical programs with variational constraints or equilibrium constraints, system of vector saddle point and system of minimax theorem are also given.     

On Noisy Extensions of Nonholonomic Constraints

We propose several stochastic extensions of nonholonomic constraints for mechanical systems and study the effects on the dynamics and on the conservation laws. Our approach relies on a stochastic extension of the Lagrange–d’Alembert framework. The mechanical system we focus on is the example of a Routh sphere, i.e., a rolling unbalanced ball on the plane. We interpret the noise in the constraint as either a stochastic motion of the plane, random slip or roughness of the surface. Without the noise, this system possesses three integrals of motion: energy, Jellet and Routh. Depending on the nature of noise in the constraint, we show that either energy, or Jellet, or both integrals can be conserved, with probability 1. We also present some exact solutions for particular types of motion in terms of stochastic integrals. Next, for an arbitrary nonholonomic system, we consider two different ways of including stochasticity in the constraints. We show that when the noise preserves the linearity of the constraints, then energy is preserved. For other types of noise in the constraint, e.g., in the case of an affine noise, the energy is not conserved. We study in detail a class of Lagrangian mechanical systems on semidirect products of Lie groups, with “rolling ball type” constraints. We conclude with numerical simulations illustrating our theories, and some pedagogical examples of noise in constraints for other nonholonomic systems popular in the literature, such as the nonholonomic particle, the rolling disk and the Chaplygin sleigh.     

Variational inclusions problems with applications to Ekeland’s variational principle,fixed point and optimization problems

In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point, existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and vector mathematical programs with variational inclusions constraints.     

A focussed review of scheduling in services

The paper first outlines the special characteristics of services, as compared to those of the manufacturing systems. The second section stresses that each of the service systems has its own major primary objective/objectives, but such primary objectives are invariably in conflict with the well-known cost-minimization objective of manufacturing systems. The paper also discusses the variety of legal, union, and budgetary constraints which must not be violated by the service-system managers under any circumstances. Finally, the paper lists eleven different types of service systems, showing for each the unique constraints, the special sets of conflicting objectives as designated by their respective managements, and the commonly used techniques, methods and procedures. The most important and the most frequently referenced articles related to each type of system are indicated.     

Job Shop Scheduling with Tooling Constraints: a Tabu Search Approach

Flexible manufacturing systems (FMSs) are automated factories in which many different part types are produced simultaneously. The tool-loading problem now adds further to the delicate task of finding an optimal schedule for such systems. In this paper, a tabu search approach is developed to solve the job shop scheduling problem with tooling constraints.