单自由度含对称约束碰振系统周期运动的转迁规律分析

利用数值仿真方法,分析了单自由度含对称弹性约束碰撞振动系统在(ω,b)参数平面内周期运动的分布及转迁规律。根据周期运动的边界条件和衔接条件理论推导得到了系统n-1-1_S周期运动存在的条件。数值仿真得到了系统在(ω,b)参数平面内的周期运动分布图,并根据各周期运动转迁的特点将参数平面划分为两个参数域,进而结合胞映射方法对各参数域内周期运动的转迁规律、周期吸引子及其吸引域的分布进行了分析;总结了各参数域内周期运动之间的相互转迁规律。     

一类相对转动系统的复杂运动及时滞速度反馈控制

研究一类典型的相对转动系统的系统参数引起的复杂运动(如混沌运动和安全域侵蚀),并对系统施加时滞速度反馈来控制系统的这些复杂动力学行为,从而保障系统的振动可靠性。利用Melnikov函数法获得时滞速度反馈控制相对转动系统产生混沌和安全域分岔的临界激励;并数值模拟了系统在不同控制参数条件下的动力学行为,从而验证了理论分析的正确性。研究结果表明,在正的反馈增益系数下,时滞速度反馈能够有效地用于控制相对转动系统的混沌运动和安全域侵蚀。     

碰撞阻尼器系统的分岔、混沌与控制

对碰撞阻尼器振动系统推导了周期解存在的条件，并利用Poincare映射和数字仿真进行了分岔与混沌运动的研究。计算结果表明，这种非线性碰撞振动系统在特定的参数条件下，除了稳定的周期运动形态外，还会沿着倍周期分岔、HOPF分岔及拟周期环面破裂等分岔进入混沌运动。因此，为了有效地利用碰撞阻尼器特性控制振动，在设计和使用碰撞阻尼器时应考虑参数满足周期运动的条件，避免由于自身的非线性特性而产生的混沌运动。     

三自由度碰撞振动系统的周期运动稳定性与分岔

建立了三自由度碰撞振动系统的动力学模型,推导出系统n-1周期运动的六维Poincar映射,根据映射Jacobi矩阵的特征值来分析n-1周期运动的稳定性。数值模拟了1-1周期运动的Hopf分岔和周期倍化分岔,进一步分析了当分岔参数变化时碰撞振动系统周期运动经拟周期分岔和周期倍化分岔向混沌的演化路径,其中有的路径是非常规的。     

含对称刚性约束振动系统的周期运动和分岔

研究了两类含对称刚性约束振动系统的周期运动和分岔。刚性约束导致两振动系统在简谐激振力作用下发生碰撞振动,并呈现不同的碰撞形式。对比两类系统的相关结果,讨论了间隙值和激振频率对两振动系统对称碰撞周期运动的稳定性和分岔的影响,分析了对称碰撞周期运动的分岔规律。对于较大的间隙值,激振频率的递减通常导致对称碰撞周期运动首先发生Neimark-Sacker分岔;对于较小的间隙值,激振频率的递减通常导致对称碰撞周期运动发生叉式分岔。研究了单周期对称碰撞运动、单周期反对称碰撞运动、单周期4-碰撞运动、倍周期4-碰撞运动和倍周期6-碰撞运动的Neimark-Sacker分岔。研究结果表明间隙值和激振频率的变化可能导致含对称刚性约束振动系统呈现复杂且形式多样的概周期碰撞运动。     

多圆盘转子系统的周期运动及其稳定性分析

采用短轴承理论方法 ,把油膜力作为转子系统的约束力加入到转子的动力学方程中 ,分析了多圆盘转子系统在非线性油膜力作用下的周期性运动及稳定性。对转子系统的周期运动 ,使用近似级数表达形式 ,对于非线性的油膜力 ,根据周期运动的特点 ,采用周期级数展开形式 ,求解了非线性动力学方程 ,得到了转子的周期运动轨道。在分析周期运动的稳定性时 ,采用谐波平衡方法 ,得到转子周期运动的稳定条件 ,为工程设计提供了一定的依据。最后对刚性非平衡对称支承单圆盘的周期运动及稳定性进行了数值模拟 ,证明了本文方法的有效性     

转子-轴承系统的非稳态分岔

通过构造非稳态分岔图，研究了转子-轴承系统在转速以一定角加速度升降时的非稳态运动。研究显示，稳态过程中产生倍周期分岔或概周期分岔的系统，相应地也将经历非稳态倍周期或概周期分岔，并且在运动形式转换时存在渗透和跳跃现象。研究揭示了渗透量与加速度的关系，并通过数值模拟，描述了运动转换的过程。     

人手操作目标物体过程运动轨迹的规律研究

根据手指生理学特性及手指间的运动特性,对三指操作单位球体运动过程进行了分析,设计了手指的运动步态模式并讨论了操作过程指尖的运动特点及指尖运动轨迹规律。采用NOKOV软件视觉捕捉系统,对手指操作过程的物体转动速度和手指运动轨迹进行了测定,并对三指转动操作运动进行解析模拟和对比。结果表明,人手操作目标物体的手指转动运动符合规划步态的运动规律。研究结果对手指重定位物体的运动仿真和手内操作的步态规划具有指导意义。     

一类冲击钻进机械系统的动力学特性

建立了一类冲击钻进机械系统的动力学模型,分析了系统周期冲击运动的类型,给出了判定系统发生钻进运动的条件,并采用数值计算的方法分析了系统的动力学行为和系统参数对系统钻进效果的影响。结果表明：擦边分岔处是系统两种截然不同运动的“分界线”,“擦边”运动导致 运动转迁为 运动或形成复杂的长周期运动或混沌;当激振频率 在 周期运动的冲击速度峰值附近时,系统具有最大冲击速度和最佳钻进量     

双质体冲击振动成型机周期运动的稳定性与全局分岔

基于Poincar映射方法对双质体冲击振动成型机的动力学行为进行了分析,讨论了单冲击周期n运动的稳定性与局部分岔。通过数值仿真研究了双质体冲击振动成型机的周期运动向混沌运动演化的全局分岔过程,分析了系统参数对单冲击周期1运动、单冲击周期2次谐运动及混沌运动的影响。     

Incremental harmonic balance method with multiple time variables for dynamical systems with cubic non‐linearities

The incremental harmonic balance method with multiple time variables is developed for analysis of almost periodic oscillations in multi‐degree‐of‐freedom dynamical systems with cubic non‐linearities, subjected to the external multi‐tone excitation. The method is formulated to treat non‐autonomous as well as autonomous dynamical systems. The almost periodic oscillations, which coexist with periodic oscillations in a rotating system model with cubic restoring force and an electromagnetic eddy‐current damper are analysed. The closed form solutions based on generalized Fourier series containing two incommensurate frequencies are obtained in the case of small non‐dimensional stiffness ratio. Almost periodic oscillations of a rotating system model in dependence on variable parameters are also analysed, where solutions are computed through an augmentation process including a greater number of harmonics and combination frequencies involved. Copyright © 2003 John Wiley & Sons, Ltd.     

汇流传动齿轮-转子-轴承系统非线性动力学分析

考虑齿侧间隙、传动误差和时变啮合刚度等非线性因素,并同时考虑滑动轴承非线性油膜力和齿轮啮合力的耦合影响,建立了汇流传动齿轮-转子-轴承系统的动力学模型。从转速方面出发,研究了齿轮系统的非线性动态响应,分析了齿轮啮合力和非线性油膜力之间的耦合作用,判断了转速变化下的油膜稳定性。结果表明：随着转速变化,系统表现出周期一运动、周期二运动、拟周期运动,混沌等丰富的动力学特性,并发现了拟周期分岔通向混沌的道路;随着转速升高,非线性啮合力和非线性油膜力先后对系统振动起到主要作用;油膜振动通过半频涡动失去了稳定性。     

结构参数对机翼非线性颤振系统混沌运动特性的影响

机翼非线性颤振系统中的混沌运动是一种复杂的非线性动力学现象,研究结构参数对机翼非线性颤振系统混沌运动特性的影响,对非线性动力学系统的混沌运动控制具有重要意义。建立具有立方型非线性操纵刚度的带操纵面二元机翼的颤振方程,采用数值积分方法分别获得该非线性颤振系统在不同阻尼水平和不同操纵刚度下的分岔特性图。对分岔特性图进行对比分析结果表明：操纵面的操纵刚度并不影响系统的混沌运动特性,而操纵面偏转自由度或机翼俯仰自由度上的阻尼将会影响系统混沌颤振区域内的周期窗口,进而影响系统的混沌运动特性,特别是两自由度中任意一个的阻尼水平减小到一定程度时,系统混沌颤振区域内的周期窗口都将会消失;但是,单一的减小某个自由度上的阻尼水平,会使机翼非线性颤振系统的颤振临界速度降低。为了使得该系统在混沌颤振区域内不产生周期窗口又不降低其颤振临界速度,可采用在减小俯仰自由度阻尼的同时增大操纵面偏转自由度阻尼的方法。     

双跨松动转子-轴承系统周期运动稳定性

建立了带有支承松动故障的具有三轴承支承双跨弹性转子-轴承系统非线性动力学模型,利用求解非线性非自治系统周期解的延拓打靶法和Floquet理论,研究了系统周期运动的稳定性及失稳规律。双跨松动转子-轴承系统响应存在着周期运动、拟周期运动和混沌运动等复杂的运动现象,系统以鞍结分岔形式失稳。在不同的转速下,系统会出现鞍结分岔和Hopf分岔等不同的分岔形式;在高转速区,松动端轴颈的运动轨迹呈现出特有的形状。研究结果为有效识别转子-轴承系统的基础松动故障提供了一定的参考。     

Pattern evocation and geometric phases in mechanical systems with symmetry

This paper is concerned with the relation between the dynamics of a given Hamiltonian system with a given symmetry group and its reduced dynamics. We illustrate the process of visualization of reduced orbits using the double spherical pendulum. In this process of visualization, one sees certain patterns when the dynamics is viewed relative to rotating frames with certain critical angular velocities. By using the reduced dynamics, we also explain these patterns. We show that if the motion on the phase space reduced by a continuous symmetry group at a given momentum level is periodic, then there is a uniformly rotating frame, that is, a one-parameter group motion, relative to which the unreduced trajectory is periodic with the same period. If the continuous symmetry group of the system is Abelian, which corresponds to the system having cyclic variables, we derive an explicit expression for the required angular velocity in terms of the dynamic phase (an average of the mechanical connection) and the geometric phase (the holonomy of the mechanical connection). We show that one can also find such a frame if the reduced orbit is quasi-periodic and a KAM (Kolmogorov-Arnold-Moser) condition is satisfied The almost periodic case is also discussed. An important aspect of this procedure is how to use it in the presence of discrete symmetries. We show that, under appropriate conditions, the visualized orbit has, relative to a suitable uniformly rotating frame, the same temporal behavior and discrete symmetries as the reduced orbit. Since these spatio-temporal patterns are not apparent with repect to most frames, we call the phenomenon pattern evocation     

Pattern evocation and geometric phases in mechanical systems with symmetry

This paper is concerned with the relation between the dynamics of a given Hamiltonian system with a given symmetry group and its reduced dynamics. We illustrate the process of visualization of reduced orbits using the double spherical pendulum. In this process of visualization, one sees certain patterns when the dynamics is viewed relative to rotating frames with certain critical angular velocities. By using the reduced dynamics, we also explain these patterns. We show that if the motion on the phase space reduced by a continuous symmetry group at a given momentum level is periodic, then there is a uniformly rotating frame, that is, a one-parameter group motion, relative to which the unreduced trajectory is periodic with the same period. If the continuous symmetry group of the system is Abelian, which corresponds to the system having cyclic variables, we derive an explicit expression for the required angular velocity in terms of the dynamic phase (an average of the mechanical connection) and the geometric phase (the holonomy of the mechanical connection). We show that one can also find such a frame if the reduced orbit is quasi-periodic and a KAM (Kolmogorov-Arnold-Moser) condition is satisfied The almost periodic case is also discussed. An important aspect of this procedure is how to use it in the presence of discrete symmetries. We show that, under appropriate conditions, the visualized orbit has, relative to a suitable uniformly rotating frame, the same temporal behavior and discrete symmetries as the reduced orbit. Since these spatio-temporal patterns are not apparent with repect to most frames, we call the phenomenon pattern evocation     

Auto-identifying Diagnostic Symptom of Nonlinear Vibration

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Rotating waves in rings of coupled oscillators

In this paper we discuss the types of stable oscillation created via Hopf bifurcations for a ring of identical nonlinear oscillators, each of which is diffusively and symmetrically coupled to both its neighbours, and which, when uncoupled, undergo a supercritical Hopf bifurcation creating a stable periodic orbit as a parameter, λ is increased. We show that for small enough coupling, the only stable rotating waves produced are either one or a conjugate pair, depending on the parity of the number of oscillators in the ring and the sign of the coupling constant, and that the magnitude of the phase difference between neighbouring oscillators for these rotating waves is either zero (i.e. the oscillators are synchronized) or the maximum possible, depending on the sign of the coupling constant. These brances of rotating waves are produced supercritically.     

Nonlinear stochastic stability analysis of wind turbine wings by Monte Carlo simulations

Wind turbines are increasing in magnitude without a proportional increase of stiffness, for which reason geometrical nonlinearities become increasingly important. In this paper the nonlinear equations of motion are analysed of a rotating Bernoulli–Euler beam including nonlinear geometrical and inertial contributions. A reduced two-degrees-of-freedom modal expansion is used specifying the modal coordinate of the fundamental blade and edgewise fixed base eigenmodes of the beam. The rotating beam is subjected to harmonic and narrow-banded support point motion from the nacelle displacement. It is shown that under harmonic excitation at certain combinations of eigenfrequencies, rotational frequency, amplitude and frequency of the support point motion, the nonlinear system may produce almost periodic response or even chaotic response. The strange attractor of this unstable behaviour is analysed under narrow-banded excitation, and it is shown that the qualitative behaviour of the strange attractor is very similar for the periodic and almost periodic responses, whereas the strange attractor for the chaotic case loses structure as the excitation becomes narrow-banded. Furthermore, the characteristic behaviour of the strange attractor is shown to be identifiable by the so-called information dimension. Due to the complexity of the coupled nonlinear structural system all analyses are carried out via Monte Carlo simulations.     

发动机对车辆振动影响的分析

本文采用局部非线性系统的脉冲响应分析方法,把整车分为线性主体和非线性局部,将车辆悬架的减振器视为非线性元件,以一个六自由度系统为整车模型,综合考虑发动机周期激励和道路不平度随机激励,借助数值计算技术分析和相应的计算机程序,从减小车架振动水平的角度,对发动机减振垫的减振作用以及发动机的转速对车架振动的影响进行分析,寻求其中的规律,以便对现代汽车的优良动力性能设计起到借鉴作用。