桥梁风致振动中的混沌现象

发布时间：2018-06-25 08:48

本文选题：非线性动力系统 + 混沌理论　；参考：《长安大学》2015年硕士论文

【摘要】：随着现代社会和经济的快速发展,桥梁工程也向着跨径更大,质量更轻,刚度更小,频率更低的方向发展。同时,风荷载已成为斜拉桥和悬索桥设计的主要控制荷载。风致振动主要分为颤振、驰振、涡振和抖振。其中,颤振与驰振均属于发散性振动,破坏性极大。涡振和抖振也严重威胁桥梁结构的耐久性和适用性。每种振动均是流固耦合造成的,机理都十分复杂,不能够单纯地用线性理论解释清楚。因此,尝试用非线性理论解释风致振动现象是具有重要意义的。混沌理论是非线性理论中最重要的理论之一,并且被广泛运用到工程实际的研究当中。因此,本文根据混沌理论,研究了风致振动的数学模型和风洞试验结果。主要工作如下。首先,本文建立桥梁结构风致振动的数学模型,得到一个四维非线性动力系统,分析无量纲风速变化引起的系统极限稳定环的改变,揭示了该系统倍周期分叉通往混沌的具体途径。此外,还研究了该动力系统的蝴蝶效应,发现微小的初始条件的差异通过该系统的迭代,最终输出完全不一样的结果。其次,本文分别介绍了闭口和开口两种典型断面的风洞试验结论。基于混沌理论,编写了李雅普诺夫指数计算的MATLAB程序,计算出不同断面主梁节段模型风洞试验加速度时程的李雅普诺夫指数,并给出了李雅普诺夫指数随风速的变化关系。研究表明,桥梁发生涡振和颤振时,加速度时程的李雅普诺夫指数均为正数,即说明涡振和颤振均属于混沌现象。另外,李雅普诺夫指数与结构阻尼比有很大的相关性。最后,本文研究了结构阻尼比、质量、风速和风攻角等因素对于李雅普诺夫指数的影响。对比分析了不同条件下的李雅普诺夫指数,结果表明:结构阻尼比对其的影响有明显规律;质量对其影响不大;风攻角对其有影响,但是没有得到明显的规律。
[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.
【学位授予单位】：长安大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U441.3

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