共查询到19条相似文献,搜索用时 281 毫秒
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应用映射的分岔理论研究塑性碰撞机械振动系统特有的两类周期碰撞运动的存在性、分岔和碰撞映射的奇异性,分析两类周期碰撞运动的规律和转迁过程。塑性碰撞振动系统的Poincaré映射具有分段不连续特性和擦边奇异性。塑性碰撞振动系统的部件在碰撞后呈现“粘贴”或“非粘贴”运动,导致该类系统的Poincaré映射具有分段不连续性;碰撞部件的擦边接触导致系统的Poincaré映射具有擦边奇异性。塑性碰撞振动系统Poincaré映射的分段不连续特性和擦边奇异性导致该类系统的周期碰撞运动发生非常规分岔。描述分段不连续性和擦边接触奇异性对系统周期运动和全局分岔的影响,分析塑性碰撞振动系统混沌运动的形成与退出过程。 相似文献
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研究了一类三自由度含间隙双边塑性碰撞振动的模型的分岔和混沌运动。建立其Poincaré映射,通过数值仿真和解析解结合的方法揭示了系统通过倍化分岔、Hopf分岔和概周期通向混沌的道路,分析了系统在分岔点附近的复杂的动力学行为。 相似文献
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以含间隙非线性赫兹接触力碰撞振动系统动力学模型为研究对象,建立了该模型的Poincaré映射,通过数值模拟,揭示了该系统在低频率、小间隙下存在非完全颤振现象,总结了系统响应从1-1-1周期运动经过Grazing分岔和Saddle-node分岔转迁到非完全颤振1-■-■运动的变化规律,数值结果表明由于初值的影响周期1-p-p运动与1-(p+1)-(p+1)运动间出现了迟滞区域共存现象。在一定的频率下基本周期1-p-p运动与1-(p+1)-(p+1)运动之间存在擦边、逆倍化分岔、混沌等运动形式,文章得出高频下对称周期运动转迁到非对称的周期运动的变化规律。 相似文献
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建立了一类三自由度振动碰撞系统的力学模型,推导了系统周期运动的解析解及Poincaré映射。基于六维Poincaré映射方法研究了系统的Hopf-pitchfork余维二分岔。在Hopf-pitchfork余维二分岔中先发生Pitchfork分岔,后发生Hopf分岔。系统通过概周期通向混沌的非常规道路揭示了在余维二分岔点附近的复杂动力学行为。 相似文献
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建立了一类三自由度冲击振动系统的周期碰撞运动及运用解析法推出了Poincaré映射的解析解。基于Poincaré映射研究系统的Hopf-Hopf余维二分岔和Hopf-flip余维二分岔。研究展现了两类余维二分岔点附近的复杂的动力学行为,揭示了在Hopf-Hopf余维二分岔中环面爆破与"水滴型"概周期吸引子通向混沌的演化过程;在Hopf-flip余维二分岔中先发生Flip分岔,后发生了周期2点的Hopf分岔并通向混沌的道路,系统参数对研究周期运动的稳定性与分岔的优化设计提供理论的参考。 相似文献
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NONLINEAR OSCILLATIONS AND CHAOS IN A RAILWAY VEHICLE SYSTEM 总被引:2,自引:0,他引:2
Zeng Jing 《机械工程学报(英文版)》1998,(3):231-238
NONLINEAROSCILLATIONSANDCHAOSINARAILWAYVEHICLESYSTEMZengJingNationalTractionPowerLaboratory,SouthwestJiaotongUniversityAbstra... 相似文献
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含松动与碰摩的转子-轴承系统非线性行为分析 总被引:2,自引:0,他引:2
以含松动与碰摩的转子-轴承系统为研究对象,采用一种新的短轴承非稳态油膜力公式和非稳态油膜转子-轴承系统碰摩的刚性约束非光滑模型建立系统的动力学方程,利用4阶Rounge-Kutta法求解非线性动力学方程,运用Mat-lab对系统进行数值模拟,通过分析相图、分岔图、Poincare截面图以及幅值谱图,得出系统丰富的非线性特性。结果表明含松动与碰摩的转子-轴承系统在工作转速较低时,轴承支座作微幅振动,随着转速增加,振动幅度也增加,在高速运转下系统处于混沌运动状态;含松动与碰摩的转子-轴承系统中松动端轴承支座在拟周期和混沌运动状态下的轴心轨迹松散,呈“柱状”结构,而未松动端在相同状态下轴心轨迹图结构紧凑,由此可以判断转子-轴承系统的松动故障。 相似文献
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Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation 总被引:1,自引:0,他引:1
SHI Peiming LIU Bin HOU Dongxiao 《机械工程学报(英文版)》2009,22(1):132-139
Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems. 相似文献
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Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability
of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves
in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker’s
Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical
transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially
consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can
be used for analyzing the behavior of NNM vibration in the Poincare Map. 相似文献
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高维含间隙振动系统的分岔与混沌研究 总被引:3,自引:2,他引:3
通过用解析法和变步长四阶Runge-Kutta数值法相结合,对一类三自由度含间隙弹性约束系统进行分析与仿真,证明三自由度含间隙系统通向混沌的道路不仅有倍周期道路和拟周期道路,而且还有包含Neimark-sacke,分岔的倍周期道路、包含叉式分岔的倍周期道路等复杂的混沌演化过程。对该系统分岔与混沌行为的研究,为工业实际中含间隙机械系统和冲击振动系统的优化设计提供理论依据。 相似文献
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NONLINEAR DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC JOURNAL BEARING-FLEXIBLE ROTOR SYSTEM 总被引:3,自引:1,他引:2
Lu Yanjun Yu Lie Liu Heng Theory of Lubrication Bearing Institue Xi'an Jiaotong University Xi'an China 《机械工程学报(英文版)》2005,18(1):58-63
The nonlinear dynamic behaviors of flexible rotor system with hydrodynamic bearing supports are analyzed. The shaft is modeled by using the finite element method that takes the effect of inertia and shear into consideration. According to the nonlinearity of the hydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique with free-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system. According to physical character of oil film, variational constrain approach is introduced to continuously revise the variational form of Reynolds equation at every step of dynamic integration and iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametric finite element method without the increasing of computing efforts. Nonlinear oil film forces and their Jacobians are simultaneously calculated and their compatible accuracy is obtained. The periodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A meth 相似文献
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考虑啮合刚度、齿侧间隙和轴承支撑间隙等因素,运用集中质量法建立了三自由度直齿圆柱齿轮副弯扭耦合非线性振动模型,并据此研究了各参数对齿轮系统非线性振动特性的影响。结果表明:齿侧间隙一定时,随着频率的升高,系统由周期运动通过激变直接进入混沌,然后又由混沌通过激变变为周期运动;在周期运动中,系统经过倍周期分岔,由双周期运动变为四周期运动,然后又通过逆倍周期分岔,由四周期运动变为双周期运动,之后又由双周期运动变为单周期运动;不同的输入转频条件下,间隙变化使系统表现出不同分岔特性,在某些特定频率下,间隙变化只增加系统响应能量变化,并不改变其动力学特性。 相似文献