共查询到19条相似文献,搜索用时 125 毫秒
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本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性. 相似文献
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非线性参数激励系统的动力分叉研究 总被引:4,自引:0,他引:4
本文针对弹性梁动力曲屈分叉问题,建立了系统的非线性Mathiue方程,较全面地讨论了此类参数激励系统的1/2亚谐分叉特性,指出以往对此类问题的研究得到的只是一种退化情形下的分叉特性,阐述了分叉方程的截断对分叉结果的影响,得到了一些新的结果。文中还介绍了一个模型弹性梁系统分叉响应特性的实测结果,证实了理论分析的可靠性。 相似文献
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参数激励与强迫激励联合作用下非线性振动系统的分叉 总被引:11,自引:2,他引:11
本文利用多尺度法研究了参数激励与强迫激励联合作用下非线性振动系统的分叉问题,给出了分叉集和八种分叉响应曲线。 相似文献
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考虑一端具有干摩擦的屈曲梁在轴向激励下的非线性振动系统,利用Floquet理论和谐波平衡法,研究了系统中初始屈曲度、阻尼、频率、激励振幅等各种物理参数对1/2业谐共振情况下倍周期分叉的影响,其规律与以往的数值模拟结果具有很好的一致性。 相似文献
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本文从群的观点出发,建立了Z3-等变的奇点理论。利用这个结果,我们讨论了非线性参数激励系统--Mathieu方程的1:3共振分叉。给出了非退化民政部下的全体分 图。数值模拟验证了我们的理论结果。 相似文献
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轴向激励作用下梁的混沌运动 总被引:4,自引:0,他引:4
本文建立了轴向激励作用下动力学模型,用多尺度法导出了系统的平均方程,并用范式理论。普适开拓及Melnikov方法了混沌运动的参数域,分析结果揭示了参激梁在退化点珠动力学特性,并在轴向激励梁的台上作了周期,根周期及混沌的实验研究,最后做了相应数值模拟。理论分析,实验研究与计算结果相吻合。 相似文献
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本文利用平均法研究了一类多频激励滞后非线性系统的组合共振,得到了该系统产生的组合共振分叉解,并讨论了该系统的奇异性,同时,本文还研究了系统参数对组合共振响应的影响,最后,数值仿真验证了本文结论的正确性。 相似文献
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一类强非线性振动系统的分叉 总被引:18,自引:0,他引:18
对于参数激励和强迫激励共同作用的一类强非线性系统,本文先用改进的L-P方法求出了变换参数,使该系统的解能展为小参数的幂级数.然后利用多尺度法求出了该系统的分叉响应方程.研究了这类强非线性系统的余维1分叉问题,画出了转迁集和分叉图 相似文献
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随机干扰与随机参数激励联合作用下的Hopf分叉 总被引:1,自引:0,他引:1
本文研究van der Pol-Duffing型的非线性振子在随机干扰和随机参数联合作用下的Hopf分叉现象。本文所得结果证实了当系统处在于Hopf分叉点附近时,对系统的参数的变化具有敏感性。在研究过程中,我们利用Markov扩散过程逼近系统的随机响应,得到了沿稳定矩的概率1稳定和矩稳定的条件。对于非线性振子,我们得到了振幅过程的稳态概论密度函数。研究发现,确定性系统的Hopf分叉点在随机参数作用下具有漂移现象,这种漂移是由系统的性质所决定的,当分叉点为超临界的,分叉点向前漂移;而当分叉点为亚临界时,这种漂移是向后的。当系统处在外部随机干扰作用下时,系统出现非零响应。另外我们发现,稳态矩的分叉与其阶数无关。 相似文献
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本文研究一类阻尼为线性,弹性恢复力为非线性的振动系统在随机外部激励作用下的随机分叉。文中采用广义稳态势和方法,求解系统响应的稳态联合概率密度函数。在此基础上根据由不变测度定义的随机分叉,讨论了具有权式分叉的确定性非线性系统在随机扰动下分叉行为。 相似文献
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A general theory for the study of degenerate Hopf bifurcation in the presence of symmetry has been carried out only in situations where the normal form equations decouple into phase/amplitude equations. In this paper we prove a theorem showing that in general we expect such degeneracies to lead to secondary torus bifurcations. We then apply this theorem to the case of degenerate Hopf bifurcation with triangular (D3) symmetry, proving that in codimension two there exist regions of parameter space where two branches of asymptotically stable 2-tori coexist but where no stable periodic solutions are present. Although this study does not lead to a theory for degenerate Hopf bifurcations in the presence of symmetry, it does present examples that would have to be accounted for by any such general theory. 相似文献
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I.IntroductionInordertostudybifurcationsofnonlineardynamicalsystemsinthedegeneratecasesofhighercodimensionnumber(>3),wemustcomputenormalformsofhigherorderfornonlineardynamicalsystems.Inrecenttwentyyearsmanyscientistsmadeveryimportantcontributionstodevelop… 相似文献
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Shunsaku Nii 《Journal of Dynamics and Differential Equations》1996,8(4):549-572
We study bifurcations, calledN-homoclinic bifurcations, which produce homoclinic orbits roundingN times (N2) in some tubular neighborhood of original homoclinic orbit. A family of vector fields undergoes such a bifurcation when it is a perturbation of a vector field with a homoclinic orbit.N-Homoclinic bifurcations are divided into two cases; one is that the linearization at the equilibrium has only real principal eigenvalues, and the other is that it has complex principal eigenvalues. We treat the former case, espcially that linearization has only one unstable eigenvalue. As main tools we use a topological method, namely, Conley index theory, which enables us to treat more degenerate cases than those studied by analytical methods. 相似文献
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Weiyao Zeng 《Journal of Dynamics and Differential Equations》1995,7(4):521-548
In this paper, we first give a sufficient condition which assures that a linear differential equation depending on a small parameter admits an exponential dichotomy onR, then we use the result obtained here on exponential dichotomies to investigate the existence of transversal homoclinic orbits of perturbed differential systems in two degenerate cases and obtain a Melnikov-type vector. The results on exponential dichotomies of this paper provide us a tool of proving the transversality of homoclinic orbits in studying degenerate bifurcations.This work is supported by NSF of China. 相似文献
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We study controllability issues for 2D and 3D Navier–Stokes (NS) systems with periodic boundary conditions. The systems are controlled by a degenerate (applied to few low modes) forcing. Methods of differential geometric/Lie algebraic control theory are used to establish global controllability of finite-dimensional Galerkin approximations of 2D and 3D NS and Euler systems, global controllability in finite-dimensional projection of 2D NS system and L2-approximate controllability for 2D NS system. Beyond these main goals we obtain results on boundedness and continuous dependence of trajectories of 2D NS system on degenerate forcing, when the space of forcings is endowed with so called relaxation metric. 相似文献
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Esteban Meca Isabel Mercader Oriol Batiste Laureano Ramírez-Piscina 《Theoretical and Computational Fluid Dynamics》2004,18(2-4):231-238
The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimension-three degenerate Takens–Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=-1. PACS 44.25.+f, 47.20.Bp, 05.45.-a 相似文献