共查询到18条相似文献,搜索用时 140 毫秒
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具有单侧刚性约束的两自由度振动系统在强共振条件下的拟周 … 总被引:6,自引:1,他引:5
采用理论分析和数值仿真相结合的方法,研究了一类两自由度碰撞振动系统在一种强共振条件下的Hopf分叉问题,分析并证实了碰撞振动系统在此共振条件下可由稳定的周期1-1振动分叉为不稳定的周期3-3振动,讨论了亚谐振动向混沌运动的演化过程。 相似文献
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含对称间隙的摩擦振子非线性动力学分析 总被引:3,自引:0,他引:3
建立了两自由度含对称间隙的干摩擦碰撞振动系统的动力学模型,分析了系统运动中存在的滑动、黏着及碰撞,分别给出其判断方法和衔接准则,推导出各阶段系统的解析解,并采用数值迭代方法求解和分析了系统的复杂动力学行为,同时分析干摩擦对系统动力学性能的影响.结果表明,系统存在叉式分叉,系统由对称周期运动变为反对称周期运动,进而通过Hopf分叉或周期倍化分叉通向混沌.在参数变化范围较大的情况下,系统存在类型丰富的周期运动、拟周期运动以及混沌;系统存在对称运动、反对称运动对、黏滑碰撞运动以及由初始条件决定的共存吸引子. 相似文献
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一类含间隙振动系统的周期运动稳定性、分岔与混沌形成过程研究 总被引:6,自引:0,他引:6
建立了两自由度含间隙振动系统对称周期碰撞运动的Poincar啨映射方程 ,讨论了该映射不动点的稳定性与局部分岔 .通过数值仿真研究了含间隙振动系统对称周期碰撞运动经叉式分岔、倍化分岔、“擦边”奇异性向混沌转迁的全局分岔过程 相似文献
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一类双自由度碰振系统运动分析 总被引:20,自引:1,他引:19
基于Poincare映射方法对一类两自由度碰撞系统进行了分析。经过详细的理论演算得到单碰周期n的次谐运动的存在性判据和稳定性条件,给出计算Jacobi矩阵特征值的公式。数值模拟表明,该方法具有令人满意的结果。此外,还讨论了当不满足所提出的单碰周期n次谐运动的存在性条件时,可能会出现的运动形式。 相似文献
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两自由度耦合van der Pol振子的拟主振动解 总被引:1,自引:0,他引:1
本文运用非线性系统的模态方法研究了两自由度耦合van der Pol振子。从退化系统稳定的主振动解出发,得到了原系统的拟主振动解,并给出了系统周期运动的条件,讨论了系统周期解、概周期解的分叉。 相似文献
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A NUMERICAL METHOD ON ESTIMATION OF STABLE REGIONS OF ROTOR SYSTEMS SUPPORTED ON LUBRICATED BEARINGS
IntroductionWhencontrollingthedynamicstabilityoflargerotatingmachinery ,notonlytheproblemwhetherequilibriumstateofthesystemisstablemustbesolved ,butalsotheregionofasymptoticstabilityneedtobedetermined .Whent→∞ ,solutionsunderinitialconditionswithinsuchre… 相似文献
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Periodic vibro-impacts and their stability of a dual component system 总被引:11,自引:0,他引:11
The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation
are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of
small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according
to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and
the bifurcation of periodic vibro-impacts is not smooth.
Project supported in part by National Natural Science Foundation of China under the grant 59572024 and in part by Trans-century
Training Program Foundation for the Talents by the State Education Commission of China 相似文献
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A methodology is first presented for analyzing long time response of periodically exited nonlinear oscillators. Namely, a systematic procedure is employed for determining periodic steady state response, including harmonic and superharmonic components. The stability analysis of the located periodic motions is also performed, utilizing results of Froquet theory. This methodology is then applied to a special class of two degree of freedom nonlinear oscillators, subjected to harmonic excitation. The numberical results presented in the second part of this study illustrate effects caused by the interaction of the modes as well as effects of the nonlinearities on the steady state response of these oscillators. In addition, sequences of bifurcations are analyzed for softening systems, leading to unbounded response of the model examined. Finally, the importance of higher harmonics on the response of systems with strongly nonlinear characteristics is investigated. 相似文献
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In this work we investigate the existence, stability and bifurcation of periodic motions in an unforced conservative two degree of freedom system. The system models the nonlinear vibrations of an elastic rod which can undergo both torsional and bending modes. Using a variety of perturbation techniques in conjunction with the computer algebra system MACSYMA, we obtain approximate expressions for a diversity of periodic motions, including nonlinear normal modes, elliptic orbits and non-local modes. The latter motions, which involve both bending and torsional motions in a 2:1 ratio, correspond to behavior previously observed in experiments by Cusumano. 相似文献
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根据Floquet理论关于线性周期系数系统解的性质及稳定性条件 ,定义了衡量非线性非自治系统周期解受扰后的衰减速率指标—稳定度。从动力系统流的概念出发 ,给出了利用非线性非自治系统稳态周期解受扰后的瞬态响应信息计算周期解稳定度的方法。以不平衡滑动轴承 弹性转子系统为例 ,说明了该方法的有效性。将稳定度等于零作为临界判据 ,该方法不仅解决了工频周期解失稳边界的确定问题 ,而且解决了渐进稳定域的估计和抗冲击扰动裕度的计算问题 相似文献
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Dynamics of a multi-DOF beam system with discontinuous support 总被引:2,自引:0,他引:2
D. H. Van Campen E. L. B. Van De Vorst J. A. W. van Der Spek A. De Kraker 《Nonlinear dynamics》1995,8(4):453-466
This paper deals with the long term behaviour of periodically excited mechanical systems consisting of linear components and local nonlinearities. The particular system investigated is a 2D pinned-pinned beam, which halfway its length is supported by a one-sided spring and excited by a periodic transversal force. The linear part of this system is modelled by means of the finite element method and subse1uently reduced using a Component Mode Synthesis method. Periodic solutions are computed by solving a two-point boundary value problem using finite differences or, alternatively, by using the shooting method. Branches of periodic solutions are followed at a changing design variable by applying a path following technique. Floquet multipliers are calculated to determine the local stability of these solutions and to identify local bifurcation points. Also stable and unstable manifolds are calculated. The long term behaviour is also investigated by means of standard numerical time integration, in particular for determining chaotic motions. In addition, the Cell Mapping technique is applied to identify periodic and chaotic solutions and their basins of attraction. An extension of the existing cell mapping methods enables to investigate systems with many degress of freedom. By means of the above methods very rich complex dynamic behaviour is demonstrated for the beam system with one-sided spring support. This behaviour is confirmed by experimental results. 相似文献
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The equations governing the response of hysteretic systems to sinusoidal forces, which are memory dependent in the classical phase space, can be given as a vector field over a suitable phase space with increased dimension. Hence, the stationary response can be studied with the aids of classical tools of nonlinear dynamics, as for example the Poincaré map. The particular system studied in the paper, based on hysteretic Masing rules, allows the reduction of the dimension of the phase space and the implementation of efficient algorithms. The paper summarises results on one degree of freedom systems and concentrates on a two degree of freedom system as the prototype of many degree of freedom systems. This system has been chosen to be in 1:3 internal resonance situation. Depending on the energy dissipation of the elements restoring force, the response may be more or less complex. The periodic response, described by frequency response curves for various levels of excitation intensity, is highly complex. The coupling produces a strong modification of the response around the first mode resonance, whereas it is negligible around the second mode. Quasi-periodic motion starts bifurcating for sufficiently high values of the excitation intensity; windows of periodic motions are embedded in the dominion of the quasi-periodic motion, as consequence of a locking frequency phenomenon. 相似文献