非线性动力系统全局分析的变胞胞映射法与转子／轴承系统的全局稳定性

在Ｐｏｉｎｃａｒｅ映射及胞映理论的基础上，提出了一种非线性动力系统全局分析的新方法－－变胞胞映射法，这种新方法改变了原胞映射法中胞在胞空间分布的不合理性及运算逻辑的不合理性，更适用于高维、大求解域非线性动力系统的求解。应用此方法，对具有非线性油膜力的Ｊｅｆｆｃｏｔ转子轴承系统进行了全局分析，绘制了系统分岔后的全局吸引域图，解释了一些工程中常见的非线性现象。     

非线性粘弹性板条高速运动时的混沌现象

本文考虑材料的粘性和非线性弹性性质，研究了高速运动时板条的混沌运动，建立了相应的非线性动力方程，利用Ｍｅｌｎｉｋｏｖ函数法给出发生混沌的临界条件，结合Ｐｏｉｎｃａｒｅ映射，相平面轨迹及时程曲线判定系统是否处于混沌状态，并对通向混沌的道路进行了讨论。     

变质量非完整系统相对运动动力学方程的积分理论

本文研究变质量非线性非完整系统相对于非惯性系动力学的积分理论，给出其Ｒｏｕｔｈ降阶法，Ｗｈｉｔｔａｋｅｒ降阶法，Ｐｏｉｎｃａｒｅ－Ｃａｒｔａｎ型积分变量关系和积分不变量。     

一种确定非线性裂纹转子解的形式的新方法

将小波变换与Ｐｏｉｎｃａｒｅ映射相结合，即用Ｐｏｉｎｃａｒｅ映射确定周期解，用谐波小波变换区分拟周期响应和混沌运动，提出了一种分析非线性裂纹转子系统解的形式随参数变化的新方法．结果表明这种方法是非常有效的，它比以前所用的计算Ｌｉａｐｕｎｏｖ指数的方法节约了计算时间，并且较易实施．     

非线性粘弹性梁在随动载荷作用下的混沌运动

计及材料的非线性弹性和粘性性质，研究了悬臂梁在自由端受随动载荷作用时的混沌运动，导出了相应的非线性动力方程，利用Ｍｅｌｎｉｋｏｖ函数法，结合Ｐｏｉｎｃａｒｅ映射、相平面轨迹和时程曲线判定系统是否处于混沌状态，并对系统通向混沌的道路进行了讨论．     

碰摩转子系统的非光滑分析

通过建立转子系统碰摩的Ｐｏｉｎｃａｒｅ映射,将对非光滑碰摩系统的研究转化为对Ｐｏｉｎｃａｒｅ映射的分析,文中主要对转子碰摩当中一类特殊的运动形式－单点碰摩下的擦边现象者了详细研究。从序列的极限理论出发分析了该映射的周期不动点的稳定性及其吸引域,得到了转子系统在接近擦边运动时解随系统参数变化的分岔情形。     

准Lagrange陀螺的混沌运动

本文讨论质量接近轴对称分布的准Ｌａｇｒａｎｇｅ陀螺的写点运动，应用Ｍｅｌｎｌｋｏｖ方法判断Ｓｍａｌｅ马蹿映射，并应用Ｐｏｉｎｃａｒｅ截面的数值计算证实混沌运动存在。     

强非线性动力系统周期解分析

给出一类强非线性动力系统周期解存在性，唯一性和稳定性的简易差别法以及周期解的摄动法。本差别法把问题归结为干扰力在相应的未扰系统振动周期上的功函数及其导数的讨论，其限制条件比现有结果弱。本摄动法可以认为是经典Ｌｉｎｄｓｔｅｄｔ－Ｐｏｉｎｃａｒｅ（Ｌ－Ｐ）法在强非线性振动系统的推广。它与Ｌ－Ｐ法的主要区别在于假设系统的振动频率为相角的非线性函数。     

非线性动力系统全局分析的有限元映射法

本文提出卫种求解非线性动力系统全局分析的新的数值方法－－有限元映射法。本方法的出发点是：在相空间给定区域内的全局分析实际上可以在确定该区域内所有点的一步映像点后，很地确定。若将相空间中给定区域在一步映作用下的过程与有限弹性体在力作用下产生位移的叮比拟，就很自然地将有限元法引入非线性系统的全局分析来进行近似分析。“插值胞映射法”实验上采用了相似的设想方法，但是本文明确提出有限元映射法的优点在于；第一     

带偏心转子陀螺体的混沌运动

本文讨论了无力矩条件下带有质量偏心轴对称转子的非对称陀螺体的运动。利用动量变量列写动力学方程,并将系统化作受周期微扰作用下的Ｅｕｌｅｒ－Ｐｏｉｎｓｏｔ运动。应用Ｍｅｌｎｉｋｏｖ方法预测系统存在Ｓｍａｌｄ马蹄意义下的混沌运动,此结论与Ｐｏｉｎｃａｒｅ截面的数值计算相符。从Ｐｏｉｎｃａｒｅ截面的相图也可明显看出转子对于双自旋卫星的姿态稳定作用。     

非线性轴承转子系统稳定性准则的研究

目前对于非线性轴承转子系统，仍普遍采用其线性化系统的对数衰减率作为系统的稳定性判据，这造成了理论和实验结果相差较大。本文对［１］中提出的ＰＣＭ法作了改进，通过对无限长滑动轴承支承对称刚性单盘转子系统的非线性稳定性规律进行的分析，揭示了上述现象的非线性本质，为建立更适用于非线性轴承转子系统的稳定性准则提供参考。     

非线性动力系统多重周期解的伪不动点追踪法

提出一种求解非线性动力系统多重周期解的新的思路和方法（伪不动点追踪法）;这一方法由寻找非线性动力系统同时存在的各个周期解间的联系入手;引入一个反映系统全局瞬态信息的标量函数,将非线性动力系统求各个周期解的问题转化为此标量函数的寻优问题．文中以布鲁塞尔振子及轴承转子系统为例。顺序求得了Ｔ,３Ｔ,４Ｔ,…周期解,从而得到了一些新的现象和结论     

Poincare型胞映射分析方法及其应用

本文用Poincare型胞映射方法对平衡及不平．衡轴承转子非线性动力系统的全局特性进行了分析研究,同时求得了一定状态空间内系统存在的周期解及其在各不同Poincare截面上的吸引域,得到了一些新的现象和规律,并通过对平衡及不平衡轴承转子系统的全局特性异同的比较,说明了要建立既适用于平衡轴承转子系统又适用于不平衡轴承转子系统的非线性稳定性准则应注意的几个问题     

推力轴承热稳定性非线性分析及周期稳态解的全局特性研究

建立了考虑瞬态油膜压力影响的热稳定性分析模型 ,用求解系统周期解分岔的 PNF法对推力轴承系统的热稳定性进行了研究 ,结合 Poincare映射与胞映射法思想 ,提出了用于分析系统周期稳态解全局特性的数值计算 PCM方法 ,并对推力轴承热系统周期稳态解的全局特性进行了考察     

Post-critical behavior of damped beam columns with variable cross section subjected to distributed follower forces

In this paper the post-critical behavior of beam columns with variable mass and stiffness properties subjected to follower forces arbitrarily distributed along their length in the presence of damping (both internal and external) is investigated using a complete nonlinear dynamic analysis. Although the static nonlinear analysis is more economical in computational cost, it is associated only with the loss of local stability via flutter or divergence. Thus, the nonlinear dynamic analysis is adopted in order to examine the global stability of the system. The governing equations of hyperbolic type are derived in terms of the displacements by considering (a) nonlinear response including the axial deformation, (b) nonlinear response excluding the axial deformation and (c) linear response. Moreover, as the cross-sectional properties of the beam vary along its axis, the resulting coupled nonlinear differential equations have variable coefficients. Their solution is achieved using the analog equation method (AEM) of Katsikadelis. Besides its accuracy and effectiveness, this method overcomes the shortcoming of a possible FEM solution which may experience a lack of convergence. The problems treated in this investigation include beam columns with various load distributions, such as constant, linear and parabolic. Some of the conclusions detected in studying the nonlinear dynamic stability of Beck’s column with variable cross section (Katsikadelis and Tsiatas, Nonlinear dynamic stability of damped Beck’s column with variable cross section. Int. J. Non-linear Mech. 42, 164–171, 2007), are also valid for the case of distributed loads. The important, however, finding is that the post-critical response under distributed loads depends on the law of distribution of mass and stiffness properties, which may lead also to explosive flutter (unbounded amplitude), in contrast to Beck’s column (end-tip load) where the motion is always bounded.     

A method for the analysis of dynamic response of structure containing non-smooth contactable interfaces

A novel single-step method is proposed for the analysis of dynamic response of visco-elastic structures containing non-smooth contactable interfaces. In the method, a two-level algorithm is employed for dealing with a nonlinear boundary condition caused by the dynamic contact of interfaces. At the first level, and explicit method is adopted to calculate nodal displacements of global viscoelastic system without considering the effect of dynamic contact of interfaces and at the second level, by introducing contact conditions of interfaces, a group of equations of lower order is derived to calculate dynamic contact normal and shear forces on the interfaces. The method is convenient and efficient for the analysis of problems of dynamic contact. The accuracy of the method is of the second order and the numerical stability condition is wider than that of other explicit methods. The project supported by the National Natural Science Foundation of China (59578032) and the Key Project of the Ninth Five-Year Plan (96221030202)     

LARGE RANGE ANALYSIS FOR NONLINEAR DYNAMIC SYSTEMS——ELEMENT MAPPING METHOD

This paper presents a new method for global analysis of nonlinear system. By means of transforming the nonlinear dynamic problems into point mapping forms which are single-valued and continuous, the state space can be regularly divided into a certain number of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping given by definition. Hence, the large range distributed problem of the mapping fixed points will be simplified as a process for solving a set of linear equations. Still further, the exact position of the fixed points can be found by the iterative technique. It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the deformation matrix of linear mapping. In this paper, the attractive kernel for the stationary fixed points is defined, which makes great advantage for describing the attractive domains of the fixed points. The new method is more convenient and effective than the cell     

LARGE RANGE ANALYSIS FOR NONLINEAR DYNAMIC SYSTEMS——ELEMENT MAPPING METHOD

This paper presents a new method for global analysis of nonlinear system. By means of transforming the nonlinear dynamic problems into point mapping forms which are single-valued and continuous, the state space can be regularly divided into a certain number of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping given by definition. Hence, the large range distributed problem of the mapping fixed points will be simplified as a process for solving a set of linear equations. Still further, the exact position of the fixed points can be found by the iterative technique. It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the deformation matrix of linear mapping. In this paper, the attractive kernel for the stationary fixed points is defined, which makes great advantage for describing the attractive domains of the fixed points. The new method is more convenient and effective than the cell mapping methodl^[1]. And an example for two-dimensional mapping is given.     

涡轮泵转子-迷宫密封系统的非线性稳定性和分岔

研究迷宫密封对某一工程涡轮泵转子系统动力特性的影响,迷宫密封力采用Muszynska非线性力模型,应用有限元法建立转子系统的动力学方程,采取系统动力学方程中包含的高阶线性自由度和低阶的非线性自由度进行分块处理的方法,有效地缩短了求解时间。根据Floquet理论,判别系统的临界失稳转速,并由Floquet乘子来确定系统失稳后分岔方式。采用分块-Newmark法数值模拟了转子二涡轮盘的轴心轨迹。最后分析了涡轮泵转子二涡轮盘的质量偏心同相位和存在90度相位差时对转子系统运动特性的影响。