本文選題：非線性動力系統(tǒng) + 混沌理論　； 參考：《長安大學(xué)》2015年碩士論文

【摘要】：隨著現(xiàn)代社會和經(jīng)濟的快速發(fā)展,橋梁工程也向著跨徑更大,質(zhì)量更輕,剛度更小,頻率更低的方向發(fā)展。同時,風(fēng)荷載已成為斜拉橋和懸索橋設(shè)計的主要控制荷載。風(fēng)致振動主要分為顫振、馳振、渦振和抖振。其中,顫振與馳振均屬于發(fā)散性振動,破壞性極大。渦振和抖振也嚴重威脅橋梁結(jié)構(gòu)的耐久性和適用性。每種振動均是流固耦合造成的,機理都十分復(fù)雜,不能夠單純地用線性理論解釋清楚。因此,嘗試用非線性理論解釋風(fēng)致振動現(xiàn)象是具有重要意義的。混沌理論是非線性理論中最重要的理論之一,并且被廣泛運用到工程實際的研究當中。因此,本文根據(jù)混沌理論,研究了風(fēng)致振動的數(shù)學(xué)模型和風(fēng)洞試驗結(jié)果。主要工作如下。首先,本文建立橋梁結(jié)構(gòu)風(fēng)致振動的數(shù)學(xué)模型,得到一個四維非線性動力系統(tǒng),分析無量綱風(fēng)速變化引起的系統(tǒng)極限穩(wěn)定環(huán)的改變,揭示了該系統(tǒng)倍周期分叉通往混沌的具體途徑。此外,還研究了該動力系統(tǒng)的蝴蝶效應(yīng),發(fā)現(xiàn)微小的初始條件的差異通過該系統(tǒng)的迭代,最終輸出完全不一樣的結(jié)果。其次,本文分別介紹了閉口和開口兩種典型斷面的風(fēng)洞試驗結(jié)論�；诨煦缋碚�,編寫了李雅普諾夫指數(shù)計算的MATLAB程序,計算出不同斷面主梁節(jié)段模型風(fēng)洞試驗加速度時程的李雅普諾夫指數(shù),并給出了李雅普諾夫指數(shù)隨風(fēng)速的變化關(guān)系。研究表明,橋梁發(fā)生渦振和顫振時,加速度時程的李雅普諾夫指數(shù)均為正數(shù),即說明渦振和顫振均屬于混沌現(xiàn)象。另外,李雅普諾夫指數(shù)與結(jié)構(gòu)阻尼比有很大的相關(guān)性。最后,本文研究了結(jié)構(gòu)阻尼比、質(zhì)量、風(fēng)速和風(fēng)攻角等因素對于李雅普諾夫指數(shù)的影響。對比分析了不同條件下的李雅普諾夫指數(shù),結(jié)果表明:結(jié)構(gòu)阻尼比對其的影響有明顯規(guī)律;質(zhì)量對其影響不大;風(fēng)攻角對其有影響,但是沒有得到明顯的規(guī)律。
[Abstract]:With the rapid development of modern society and economy, bridge engineering is developing towards the direction of larger span, lighter mass, smaller stiffness and lower frequency. At the same time, wind load has become the main control load of cable-stayed bridge and suspension bridge design. Wind-induced vibration is mainly divided into flutter, galloping, vortex and buffeting. Among them, flutter and galloping both belong to divergent vibration, which is extremely destructive. Vortex vibration and buffeting also seriously threaten the durability and applicability of bridge structures. Each vibration is caused by fluid-solid coupling, and the mechanism is very complicated, which can not be explained clearly by linear theory. Therefore, it is of great significance to try to explain the wind-induced vibration with nonlinear theory. Chaos theory is one of the most important theories in nonlinear theory and is widely used in engineering practice. Therefore, according to the chaos theory, the mathematical model of wind-induced vibration and the results of wind tunnel test are studied in this paper. The main work is as follows. First of all, the mathematical model of wind-induced vibration of bridge structure is established, and a four-dimensional nonlinear dynamic system is obtained. The change of limit stability cycle caused by the change of dimensionless wind speed is analyzed. The specific path to chaos of the double period bifurcation of the system is revealed. In addition, the butterfly effect of the dynamic system is studied. It is found that the tiny difference of initial conditions is obtained by the iteration of the system, and the final result is completely different. Secondly, the wind tunnel test results of two typical sections, closed and open, are introduced in this paper. Based on the chaos theory, a MATLAB program for calculating Lyapunov exponents is compiled, and the Lyapunov exponents of the acceleration history of wind tunnel tests in different sections are calculated, and the relationship between Lyapunov exponents and wind speed is given. The results show that the Lyapunov exponents of the acceleration time history are all positive numbers when the vortex vibration and flutter of the bridge occur, which means that both the vortex vibration and the flutter are chaotic phenomena. In addition, Lyapunov exponent has great correlation with damping ratio of structure. Finally, the effects of damping ratio, mass, wind speed and angle of attack on Lyapunov exponent are studied. The Lyapunov exponents under different conditions are compared and analyzed. The results show that the damping ratio of the structure has an obvious law, the mass has little effect on it, and the angle of attack has an effect on it, but there is no obvious rule.
【學(xué)位授予單位】：長安大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：U441.3

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