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RESEARCH IN STABILITY OF PERIODIC MOTION,BIFURCATION AND CHAOS IN A VIBRATORY SYSTEM WITH A CLEARANCE 总被引:1,自引:0,他引:1
LuoGuanwei XieJianhua 《Acta Mechanica Solida Sinica》2003,16(2):127-133
A two-degrees-of-freedom vibratory system with a clearance or gap is under consideration based on the Poincard map. Stability and local bifurcation of the period-one doubleimpact symmetrical motion of the system are analyzed by using the equation of map. The routes from periodic impact motions to chaos, via pitchfork bifurcation, period-doubling bifurcation and grazing bifurcation, are studied by numerical simulation. Under suitable system parameter conditions, Neimark-Sacker bifurcations associated with periodic impact motion can occur in the two-degrees-of-freedom vibro-impact system. 相似文献
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本文对苏联巴尔坎(Д.Д.Баркан)所提出的有关振动锤计算的假设和方法做了某些修正.修正后的计算方法能更全面、准确地描述振动锤的工作过程. 相似文献
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Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated. 相似文献
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以弹性弦的长度变化不可忽略为条件,简要推导了一般振幅下的弦的振动方程。结果显示,弦的振动情形是复杂的,但在此条件下得到的弦振动方程比小振幅条件下的方程具有更真实的物理意义,且后者是前者的极限简单情形,指出了横振动可以向纵振动转化,此推导过程可以使人们更好的理解弦的振动。 相似文献
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求匀质杆纵向振动的行波法陈立群(上海交通大学,上海200030)对于连续体的振动,机械振动教材中通常用分离变量法(驻波法)来研究,将连续体的振动视为无限多个驻波的叠加.这里我们将行波法应用于匀质杆的纵向振动,因而可知有限连续体的振动也可视为无限多个行... 相似文献
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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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达朗贝尔法和分离变量法是求解弦、杆、轴的自由振动微分方程(波动方程)的两种基本方法;达朗贝尔法把振动位移处理成运动方向相反的两组无限多个行波的叠加,分离变量法则把振动位移处理成无限多个驻波的叠加,所以亦称前者为行波法,称后者为驻波法.这两种方法所得到... 相似文献
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把特征向量的各阶导数表示成所有模态的线性组合,并利用左模态与右模态间的双正交性,首先导出了任意非亏损矩阵的重特征值的一阶导数所满足的特征值问题,然后根据此特征值问题无、看重根的情况,再导出了异导重特征值和等导重特征值对应的可微特征向量、特征值和特征向量各阶导数的一般计算公式。算例显示了方法的正确性。 相似文献
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线性振动亏损系统广义模态参数的识别方法 总被引:2,自引:0,他引:2
基于线性振动亏损系统的广义模态理论,本文提出了一种识别亏损系统广义模态参数的频域方法。该方法将直接法与迭代法相结合,无需人工初值,可分步识别出亏损系统的全部广义模态参数。模拟识别结果表明,本文方法是有效且可行的。 相似文献
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Based on the generalized mode theory of linear vibrating defective systems, an identification method of generalized modal parameters is presented in this paper. By the use of this method, which combines the direct method with the iteration method in frequency domain, all the generalized modal parameters can be identified without any initial value. It is shown that the present method is effective and useful. 相似文献
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利用奇异值分解方法来讨论系统广义模态的可控可观性的量度问题,得到了亏损系统广义模态可控可观性的量度指标,同时用实例说明了本文方法是有效的。 相似文献
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Principal trajectories of forced vibration of linear and nonlinear continuous systems are introduced as such motions in which the system is equivalent to a Newtonian particle in the function space of the system configurations. The corresponding 'effective mass' of the particle gives physical characteristics of the system response, so that zero effective mass is associated with resonance. The methodology can be viewed as a complementary tool to the method of normal modes, when considering the class of forced vibrating systems, since the related basis accounts for the system physical properties as well as the external forcing factor. In particular, it is shown that a two degrees of freedom system can possess an infinite discrete set of in-phase and out-of-phase forced vibrations of the normal modes type. The corresponding forcing vector-functions obey the second Newton law due to the definition of principal trajectories. 相似文献