共查询到17条相似文献,搜索用时 125 毫秒
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求强非线性系统次谐共振解的MLP方法 总被引:10,自引:0,他引:10
定义了一个新的参数变换α=α(ε,nω0/m,ω1),扩展了改进的LP方法的应用范围,使该方法能够求强非线性系统的次谐共振解.研究了Duffing方程的1/3亚谐和3次超谐共振解以及Vander Pol-Mathieu方程1/2亚谐共振解,这些例子说明近似解和数值解相当吻合. 相似文献
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研究了转子-密封系统在气流激振力作用下的低频振动——1∶2亚谐共振现象.利用流体计算动力学(CFD)方法对转子-密封系统进行了流场模拟计算,辨识出适用于气流流场的Muszynska模型参数,并建立了转子-密封系统动力学方程.采用多尺度方法将系统进行3次截断,并得到系统响应.采用奇异性理论研究了系统的1∶2亚谐共振,进一步得到系统亚谐共振的分岔方程和转迁集,根据转迁集给出了在不同奇异性参数空间内的分岔图.同时,由分岔方程得到了亚谐共振非零解存在的条件.其分析结果对抑制转子-密封系统的亚谐振动有重要的工程意义. 相似文献
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通过谐波平衡法和数值积分法研究了杜芬方程的1/3纯亚谐解.提出假设解,找出了亚谐频域,并对参数变化的过渡过程的敏感性和初始值扰动的过渡过程进行了研究.考察了亚谐响应幅值系数对阻尼的敏感性及亚谐振动谐波成分的渐近稳态性.此外,运用广义分形理论对杜芬方程纯亚谐解过渡过程进行了分析.分析表明,广义维数的敏感维数能清楚地描述杜芬方程纯亚谐解过渡过程特征;并对改变初始扰动、阻尼系数、激励幅值情况下,其两个不同频域的杜芬方程纯亚谐解过渡过程的不同分形特性显现出敏感性. 相似文献
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本文提出了处理平面Hamilton系统在小扰动下次谐和超次谐解的方法.利用这个方法对一类系统进行了 处理,发现理论与数值 结果较好地吻合. 相似文献
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本文研究在简谐激励力作用下二端面弹性转轴相对转动的主共振、超谐波共振和亚谐波共振.用平均法研究了系统的主共振,得到了系统的渐进稳态周期解,采用多尺度法求得了系统的3次超谐波共振解和1/3次亚谐波共振解. 相似文献
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殷红燕 《纯粹数学与应用数学》2014,(3):240-244
研究了小周期扰动对一类存在Hopf分支的非线性系统的影响.特别是应用平均法讨论了扰动频率与Hopf分支固有频率在共振及二阶次调和共振的情形周期解分支的存在性.表明了在某些参数区域内,系统存在调和解分支和次调和解分支,并进一步讨论了二阶次调和分支周期解的稳定性. 相似文献
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《非线性Mathieu方程亚谐共振分叉理论》的一些推广 总被引:2,自引:1,他引:1
在文[1]中,作者讨论了非线性Mathieu方程的亚谐共振分叉理论,得到的主要结果是,在参数α-β平面上,具有六种不同拓扑结构的分叉图.本文摧广了这一结果,指出:如果选取不同的芽来计算同样的分叉问题,则可以有十四种不同拓扑结构的分叉图. 相似文献
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Jakob J. Keller 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1976,7(3):303-323
Summary The third order resonance effects in a closed tube are investigated. Third order subharmonic resonance solutions are found when the frequency of the driving piston motion lies near a third of a resonant frequency. To obtain a survey over this kind of solutions, some signals are calculated. The second order corrections of Chester's resonance solutions are given. These are of the order 0(M); the shock strength of the third order subharmonic solutions is of the order 0(M
3/2).
Zusammenfassung Die Resonanzeffekte dritter Ordnung in einem geschlossenen Rohr werden untersucht. Es werden subharmonische Lösungen dritter Ordnung gefunden, wenn die Frequenz der antreibenden Kolbenbewegung in einer kleinen Umgebung eines Drittels einer Resonanzfrequenz liegt. Um einen Ueberblick über Lösungen dieser Art zu gewinnen, sind einige Signale berechnet worden. Die Korrekturen zweiter Ordnung von Chesters Resonanzlösung werden angegeben. Diese haben die Grössenordnung 0(M); die Stösse der subharmonischen Lösungen dritter Ordnung sind von der Grössenordnung 0(M 3/2).相似文献
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Temple H. Fay Sarah Duncan Graham 《International Journal of Mathematical Education in Science & Technology》2013,44(1):65-79
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke's Law, the motion of each weight is described by a fourth-order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project. 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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Ruyuan Zhang Junjie Wei Jianhong Wu 《Journal of Mathematical Analysis and Applications》2002,276(2):477-496
We consider the multiplicity and stability of subharmonic solutions of discrete dynamic systems with periodic perturbations, whose existence was established in the first part of this series. Under the hypotheses that the perturbation is locally Lipschitz continuous, we determine the precise number of subharmonic solutions, and we also show that these subharmonic solutions are stable (unstable) provide the periodic orbit of the unperturbed system is stable (unstable). 相似文献
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讨论一类三维系统在周期扰动下的分支问题.假设此三维系统有一族闭轨,利用 Poincar\'e映射及积分流形定理,得到了在周期扰动下由这族闭轨产生次调和解和不变环面的条件,并讨论了次调和解的鞍结点分支. 相似文献