共查询到20条相似文献,搜索用时 109 毫秒
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时滞速度反馈对强迫自持系统动力学行为的影响 总被引:3,自引:0,他引:3
研究强迫自持振动系统因时滞反馈产生的主共振解及其分岔.通过对强迫非自治系统的时滞反馈控制,得到所要研究的数学模型.讨论对应的线性化系统使平凡平衡态失稳出现周期解的稳定性临界条件.特别关注主共振及分岔.结果表明,稳定的主共振解随着时滞的变化周期性地出现在系统中.同时,也给出了不稳定的主共振关于时滞变化的区域,在理论方面给出了系统出现概周期运动的时滞区域.数据模拟证实了理论结果. 相似文献
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流体诱发水平悬臂输液管的内共振和模态转换(Ⅱ) 总被引:1,自引:1,他引:0
基于得到的水平悬臂输液管非线性动力学控制方程,详细研究了由流速最小临界值诱发的3∶1内共振.通过观察内共振调谐参数、主共振调谐参数和外激励幅值的变化,发现在内共振临界流速附近,流速导致系统出现模态转换、鞍结分岔、Hopf分岔、余维2分岔和倍周期分岔等非线性动力学行为,对应的管道系统的周期运动失稳出现跳跃、颤振和更加复杂的动力学行为.通过理论结果与数值模拟比较,表明了理论分析的有效性和正确性. 相似文献
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分数阶Maxwell模型可用来模拟粘弹性的海床淤泥.与传统的有理分式模型相比,分数阶Maxwell模型可以用更少的自由参数,较好地描述某些真实淤泥的流变特性.将该分数阶Maxwell模型用于研究淤泥与自由表面水波的相互作用,并得到了线形单色波的衰减率.从水波衰减率曲线中可观测到淤泥层的共振现象,共振时衰减率将达到峰值.对于线形单色波,其衰减率还可表示为各模态衰减率之和,从而可研究某一模态的运动对水波衰减的影响.模态分析表明,当某一模态运动引发共振时,总衰减率由该模态的模态衰减率决定. 相似文献
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本论文研究了两个自由度分段线性振动系统的亚谐解,其理论结果证明系统可能存在各种类型的亚谐解[(1.31)~(1.34)],如1/2,1/3,1/4,1/5,1/6,…亚谐共振解在模拟计算机的计算结果以及现场实验的结果中得到了部分证实。在一定的系统参数的情况下,模拟计算机的结果有浑沌现象发生。 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2010,15(12):4219-4229
The dynamic behavior and chaotic motion of a string-beam coupled system subjected to parametric excitation are investigated. The case of three-to-one internal resonance between the modes of the beam and the string, in the presence of subharmonic resonance for the beam is considered and examined. The method of multiple scales is applied to study the steady-state response and the stability of the string-beam coupled system at resonance conditions. Numerical simulations illustrated that multiple-valued solutions, jump phenomenon, hardening and softening nonlinearities occur in the resonant frequency response curves. The effects of different parameters on system behavior have been studied applying frequency response function. Results are compared to previously published work. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2006,11(2):203-232
In this paper, the nonlinear behavior of a one-dimensional model of the disc brake pad is examined. The contact normal force between the disc brake pad lining and rotor is represented by a second order polynomial of the relative displacement between the two elastic bodies. The frictional force due to the sliding motion of the rotor against the stationary pad is modeled as a distributed follower-type axial load with time-dependent terms. By Galerkin discretization, the equation governing the transverse motion of the beam model is reduced to a set of extended Duffing system with quasi-periodically modulated excitations. Retaining the first two vibration modes in the governing equations, frequency response curves are obtained by applying a two-dimensional spectral balance method. For the first time, it is predicted that nonlinearity resulting from the contact mechanics between the disc brake pad lining and rotor can lead to a possible irregular motion (chaotic vibration) of the pad in the neighborhood of simple and parametric resonance. This chaotic behavior is identified and quantitatively measured by examining the Poincaré maps, Fourier spectra, and Lyapunov exponents. It is also found that these chaotic motions emerge as a result of successive Hopf bifurcations characterized by the torus breakdown and torus doubling routes as the excitation frequency varies. Various aspects of the numerical difficulties in the solution of the nonlinear equations are also discussed. 相似文献
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V. G. Zadorozhniy 《Computational Mathematics and Mathematical Physics》2013,53(4):486-502
For three-dimensional vortex motion, a linear mathematical model with random coefficients is considered, and formulas for the first two moment functions of solutions are derived. The conditions are found under which a linear chaotic resonance occurs; i.e., the mean angular velocity of the motion increases. The results show that the energy of the vortex increases because of the chaotic motions present in the flow. 相似文献
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A. P. Markeev 《Proceedings of the Steklov Institute of Mathematics》2016,295(1):190-201
The inertial motion of a material point is analyzed in a plane domain bounded by two curves that are coaxial segments of an ellipse. The collisions of the point with the boundary curves are assumed to be absolutely elastic. There exists a periodic motion of the point that is described by a two-link trajectory lying on a straight line segment passed twice within the period. This segment is orthogonal to both boundary curves at its endpoints. The nonlinear problem of stability of this trajectory is analyzed. The stability and instability conditions are obtained for almost all values of two dimensionless parameters of the problem. 相似文献
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This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the “reversible pitch-fork” bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2008,13(2):400-406
We study motion of an one-dimensional Hamiltonian oscillator driven by an external force which is periodic in time and in coordinate as well. It is shown that dynamics of the oscillator is strongly affected by the resonance between spatial and temporal oscillations of the perturbation imposed. In particular, this resonance can induce strong but bounded chaotic diffusion in certain areas of phase space. The model of the Duffing oscillator is used as an example for the numerical simulation. 相似文献
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J. Awrejcewicz 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1989,40(3):375-386
The Hopf bifurcation curves for the averaged system of second order differential equations are obtained using an analytical method. Numerical experiments have proved the existence of chaotic motion in the vicinity of these curves. For the different parameter sets, two very similar types of evolution of strange attractors are presented. 相似文献
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In this paper, a nonlinear Euler-Bernoulli beam under a concentrated harmonic excitation with intermediate nonlinear support is investigated. Continuous expression for the kinetic energy, potential energy and dissipation function are constructed. An energy method based on the Lagrange equation combined with the Galerkin truncation is used for discretizing the governing equation. The Multi-dimensional incremental harmonic balance method (MIHBM) is derived, and the comparisons between the numerical results and the approximate analytical solutions based on the MIHBM verify the excellent accuracy of the MIHBM. The steady state dynamic of the beam is investigated by MIHBM. In order to investigate the energy transmission and understand the vibration response of the Euler-Bernoulli beam, the effects of the key parameters on the dynamic behaviors are studied and discussed, individually. The results show that the amplitude-frequency curves exhibits softening nonlinear behavior in the super-harmonic resonance region, and near resonant region the hardening nonlinear behavior is observed depending on the different parameters. Nonlinear dynamic analysis, such as bifurcation, 3-D frequency spectrum, waveform, frequency spectrum, phase diagram and Poincaré map, are also presented in order to study the influences of the key parameters on the vibration behaviors for the beam in a more accurate manner. In addition, the path to chaotic motion is observed to be through a sequence of the periodic motion and quasi-periodic motion. 相似文献
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《Chaos, solitons, and fractals》2006,27(1):175-186
In this paper, we investigate the Shilnikov type multi-pulse chaotic dynamics for a rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The stiffness in the AMB is considered as the time-varying in a periodic form. The dimensionless equation of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions is a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities and parametric excitation. The asymptotic perturbation method is used to obtain the averaged equations in the case of primary parametric resonance and 1/2 subharmonic resonance. It is found from the numerical results that there are the phenomena of the Shilnikov type multi-pulse chaotic motions for the rotor-AMB system. A new jumping phenomenon is discovered in the rotor-AMB system with the time-varying stiffness. 相似文献
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Long-Jye Sheu Hsien-Keng Chen Juhn-Horng Chen Lap-Mou Tam 《Chaos, solitons, and fractals》2007,31(5):1203-1212
The dynamics of fractional-order systems have attracted a great deal of attentions in recent years. With fractional order, the dynamics of a system which includes comprehensive dynamical behaviors, such as fixed point, periodic motion, chaotic motion, and transient chaos is studied numerically in this paper. It is known that chaos exists in the fractional-order system with order less than 3. In this study, the lowest order found for this system to yield chaos is 2.43. The results are validated by the existence of a positive Lyapunov exponent. Period doubling routes to chaos in the fractional-order system are also obtained. Moreover, generation of a four-scroll chaotic attractor by the system is observed. 相似文献