本文選題：多時(shí)間尺度　切入點(diǎn)：混合模式振動(dòng)　出處：《江蘇大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：多時(shí)間尺度混合模式振動(dòng)問(wèn)題具有廣泛的工程背景,探討混合模式振動(dòng)各種可能的誘發(fā)機(jī)制并對(duì)其進(jìn)行分類(lèi)是非線性科學(xué)的前沿和熱點(diǎn)問(wèn)題之一。本論文以Rayleigh系統(tǒng)、Duffing系統(tǒng)以及van der Pol-Duffing等經(jīng)典的非線性系統(tǒng)為例,應(yīng)用分岔理論,頻率轉(zhuǎn)換快慢分析法以及數(shù)值模擬等方法,揭示了通向混合模式振動(dòng)的多種新路徑,即吸引子的“極速逃逸”機(jī)制、滯后曲線的曲折機(jī)制以及延遲分岔機(jī)制。主要內(nèi)容如下:第一章,介紹了非線性動(dòng)力學(xué)的發(fā)展歷程,多尺度問(wèn)題的背景和現(xiàn)狀,本文所涉及的分岔類(lèi)型和研究方法,以及本文的主要工作內(nèi)容。第二章,揭示了多頻激勵(lì)Rayleigh系統(tǒng)中經(jīng)由吸引子的“極速逃逸”機(jī)制而誘發(fā)的混合模式振動(dòng)�？熳酉到y(tǒng)的兩個(gè)臨界值限制了周期吸引子或平衡點(diǎn)吸引子的區(qū)域,其外部是發(fā)散區(qū)域。當(dāng)控制參數(shù)達(dá)到臨界值時(shí),周期吸引子和平衡點(diǎn)吸引子能夠快速遠(yuǎn)離其初始位置。由此,揭示了誘發(fā)混合模式振動(dòng)的新機(jī)制,即所謂的吸引子的“極速逃逸”機(jī)制;同時(shí),得到了點(diǎn)-點(diǎn)型和圈-圈型兩類(lèi)新型的混合模式振動(dòng)。第三章,研究了多頻激勵(lì)下的Duffing系統(tǒng)的復(fù)雜動(dòng)力學(xué)行為,得到了經(jīng)由滯后曲線的曲折而誘發(fā)的混合模式振動(dòng)。研究表明,快子系統(tǒng)的平衡點(diǎn)曲線會(huì)不斷地曲折,這導(dǎo)致混合模式振動(dòng)的準(zhǔn)靜態(tài)過(guò)程產(chǎn)生了明顯的振蕩行為�；诖�,得到了通向混合模式振動(dòng)的新路徑,即滯后的曲折機(jī)制。此外,探討了激勵(lì)頻率和振幅對(duì)混合模式振動(dòng)行為的影響。研究表明,混合模式振動(dòng)的三個(gè)頻率分量由激勵(lì)頻率決定,而混合模式振動(dòng)的轉(zhuǎn)遷則由激勵(lì)振幅決定。第四章,基于延遲Hopf分岔,揭示了通向混合模式振動(dòng)的新路徑,由此得到了兩類(lèi)新的混合模式振動(dòng),即組合式“延遲supHopf/fold cycle”-“subHopf/supHopf”型混合模式振動(dòng)以及經(jīng)由“延遲supHopf/supHopf”滯后環(huán)而誘發(fā)的“subHopf/supHopf”型混合模式振動(dòng)。研究表明,延遲Hopf分岔在混合模式振動(dòng)產(chǎn)生的過(guò)程中起到了決定性的作用,這不僅豐富了通向混合模式振動(dòng)的道路,同時(shí)也深化了對(duì)混合模式振動(dòng)的動(dòng)力學(xué)機(jī)制的理解。第五章,對(duì)本文的結(jié)果進(jìn)行總結(jié),并對(duì)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.
【學(xué)位授予單位】：江蘇大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O19

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