关于通向混合模式振动的几类新路径的探讨

发布时间：2018-03-03 23:08

本文选题：多时间尺度　切入点：混合模式振动　出处：《江苏大学》2017年硕士论文　论文类型：学位论文

【摘要】：多时间尺度混合模式振动问题具有广泛的工程背景,探讨混合模式振动各种可能的诱发机制并对其进行分类是非线性科学的前沿和热点问题之一。本论文以Rayleigh系统、Duffing系统以及van der Pol-Duffing等经典的非线性系统为例,应用分岔理论,频率转换快慢分析法以及数值模拟等方法,揭示了通向混合模式振动的多种新路径,即吸引子的“极速逃逸”机制、滞后曲线的曲折机制以及延迟分岔机制。主要内容如下:第一章,介绍了非线性动力学的发展历程,多尺度问题的背景和现状,本文所涉及的分岔类型和研究方法,以及本文的主要工作内容。第二章,揭示了多频激励Rayleigh系统中经由吸引子的“极速逃逸”机制而诱发的混合模式振动。快子系统的两个临界值限制了周期吸引子或平衡点吸引子的区域,其外部是发散区域。当控制参数达到临界值时,周期吸引子和平衡点吸引子能够快速远离其初始位置。由此,揭示了诱发混合模式振动的新机制,即所谓的吸引子的“极速逃逸”机制;同时,得到了点-点型和圈-圈型两类新型的混合模式振动。第三章,研究了多频激励下的Duffing系统的复杂动力学行为,得到了经由滞后曲线的曲折而诱发的混合模式振动。研究表明,快子系统的平衡点曲线会不断地曲折,这导致混合模式振动的准静态过程产生了明显的振荡行为。基于此,得到了通向混合模式振动的新路径,即滞后的曲折机制。此外,探讨了激励频率和振幅对混合模式振动行为的影响。研究表明,混合模式振动的三个频率分量由激励频率决定,而混合模式振动的转迁则由激励振幅决定。第四章,基于延迟Hopf分岔,揭示了通向混合模式振动的新路径,由此得到了两类新的混合模式振动,即组合式“延迟supHopf/fold cycle”-“subHopf/supHopf”型混合模式振动以及经由“延迟supHopf/supHopf”滞后环而诱发的“subHopf/supHopf”型混合模式振动。研究表明,延迟Hopf分岔在混合模式振动产生的过程中起到了决定性的作用,这不仅丰富了通向混合模式振动的道路,同时也深化了对混合模式振动的动力学机制的理解。第五章,对本文的结果进行总结,并对今后的工作提出展望。
[Abstract]:The multi-time scale mixed mode vibration problem has a wide engineering background. It is one of the leading and hot issues in nonlinear science to study and classify the possible inductive mechanisms of mixed mode vibration. In this paper, the bifurcation theory is applied to the classical nonlinear systems such as Rayleigh system duffing system and van der Pol-Duffing. The frequency conversion fast and slow analysis method and numerical simulation have revealed many new paths to the mixed mode vibration, that is, the "extreme velocity escape" mechanism of the attractor. The main contents are as follows: in Chapter 1, the development of nonlinear dynamics, the background and present situation of multi-scale problems, the types of bifurcation and the research methods involved in this paper are introduced. And the main work of this paper. Chapter two, The mixed mode vibration induced by the "extreme escape" mechanism of the attractor in a multi-frequency excited Rayleigh system is revealed. Two critical values of the fast subsystem limit the region of the periodic attractor or the equilibrium attractor. When the control parameters reach the critical value, the periodic attractor and the equilibrium attractor can move away from their initial position quickly. Thus, a new mechanism of inducing mixed mode vibration is revealed. The so-called "extreme escape" mechanism of the attractor is called, at the same time, two new types of mixed mode vibration, point-point type and cyclopyclic type, are obtained. In chapter 3, the complex dynamical behavior of the Duffing system under multi-frequency excitation is studied. The mixed mode vibration induced by the zigzag of the hysteresis curve is obtained. It is shown that the equilibrium curve of the fast subsystem will continue to twists and turns, which leads to the obvious oscillation behavior in the quasi-static process of the mixed mode vibration. A new path to mixed mode vibration, that is, the tortuous mechanism of lag, is obtained. In addition, the effects of excitation frequency and amplitude on the vibration behavior of mixed mode are discussed. It is shown that the three frequency components of mixed mode vibration are determined by the excitation frequency. The transition of mixed mode vibration is determined by the excitation amplitude. In Chapter 4th, based on the delayed Hopf bifurcation, a new path to the mixed mode vibration is revealed, and two new types of mixed mode vibration are obtained. That is, the combined "delayed supHopf/fold cycle"-"subHopf/supHopf" mixed mode vibration and the "subHopf/supHopf" mixed mode vibration induced by the "delayed supHopf/supHopf" hysteresis loop. The results show that the delayed Hopf bifurcation plays a decisive role in the process of the mixed mode vibration. This not only enriches the road to mixed mode vibration, but also deepens the understanding of the dynamic mechanism of mixed mode vibration. Chapter 5th summarizes the results of this paper and puts forward the prospects for future work.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19

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