大跨度桥梁断面非线性自激气动力与非线性气动稳定性研究
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摘要
本论文回顾了大跨度桥梁抗风研究的发展,总结了线性与非线性自激气动力的研究现状。基于平衡位置的Taylor展开,建立了简谐运动下非线性自激力气动力的数学模型。采用特殊风洞试验技术,获得了大振幅条件下薄翼和流线型箱梁断面的非线性自激气动力。探讨了典型状态下自激气动力的非线性特性和气动迟滞效应,提出了非线性气动参数的识别方法。利用非线性自激气动力开展了桥梁断面在特定条件下的非线性颤振分析。本文的主要研究内容有：
1.回顾了大跨度桥梁抗风研究的发展,总结了线性与非线性气动力的研究现状。
2.基于平衡位置的Taylor展开,推导了单自由度运动和弯扭耦合运动条件下非线性自激气动力的复数和实数表达式,建立了由多个谐波分量所组成的非线性自激气动力模型。
3.采用特殊风洞试验技术,开展了大振幅条件下薄翼和流线型箱梁断面的自激力测试,发现了自激力频谱中存在显著的高次谐波分量,验证了非线性自激力是由多个谐波分量所组成的理论结果。发现了自激气动力中非线性分量的幅值随断面运动振幅的增大而增大,随折算风速的增大而减小的一般性规律。
4.研究了流线型箱梁断面非线性自激气动力的迟滞效应。发现箱梁的气动力矩迟滞曲线在一定条件下也能转变为面积相当的“8字环”,该现象表明气动力矩在一个周期内既做了正功,也做了负功。探讨了大跨度桥梁在大振幅条件下可能出现的运行形式。
5.提出了非线性气动参数的识别方法。该方法采用直接提取的谐波参数为初始值,结合非线性最小二乘迭代算法实现。研究了不同形式的噪声对参数识别精度的影响,并指出致使信号发生偏移的噪声对识别结果有较大影响,将直接导致结果失真或不可用。
6.利用非线性自激气动力和四阶龙格-库塔算法,进行了特定条件下箱梁断面的非线性气动稳定分析,发现大跨度桥梁在“颤振后”状态,可能存在收敛、发散和等幅振动三种运动形式。探讨了非线性气动微分方程中参数的变化对运动形式以及气动稳定性的可能影响；简要探讨了紊流风对气动稳定性的影响；结合气动力的非线性特性,解释了大跨度桥梁的“硬颤振”和“软颤振”现象。
7.展望了非线性气动力今后的研究内容和方向。
This thesis reviewed the research of wind effects on the long span bridge, and summarized the current research on the linear and nonlinear Motion-Induced Aerodynamic Force (MIAF). Firstly, based on Taylor expansion of the equilibrium position, the mathematical model of nonlinear MIAF was developed under harmonic motions. Then, through the special wind tunnel tests, the nonlinear MIAF of thin airfoil and streamline box girder were obtained under the large amplitude oscillation, and the characteristics of nonlinear MIAF and aerodynamic hysteresis of the thin airfoil and streamline box girder were also discussed. In addition, the identification method of nonlinear aerodynamic parameters in the expression was proposed. Finally, the nonlinear aerodynamic analysis has been conducted using the nonlinear MIAF.
The thesis research contains following contents:
1. Reviewed the researches of wind effects on long span bridges, and summarized the current researches on the linear and nonlinear MIAF.
2. Based on Taylor expansion of the equilibrium position, deduced the plural and real expression of nonlinear MIAF under1DOF and2DOF harmonic motions, and established the nonlinear MIAF mathematical model composed of multiple harmonic components.
3. Through the special wind tunnel technology, conducted the tests of nonlinear MIAF of the thin airfoil and streamline box girder under the large amplitude oscillation, and found the remarkable higher harmonic components in the spectrum, which validated the theory that the nonlinear MIAF composed of multiple harmonic components. Discovered that the amplitude of nonlinear components in the MIAF increased with the increase of oscillation amplitude, and decreased with the increase of reduced velocity.
4. Studied the characteristics of nonlinear MIAF and aerodynamic hysteresis, and found the exist of "figure8" loop in the aerodynamic moment hysteresis curve of the streamline box girder, that is, the aerodynamic moment has done not only positive work but also negative work in one period. Then discussed the possible vibration status of long span bridges under the large amplitude oscillation.
5. Proposed the identification method of nonlinear aerodynamic parameters. This method could realized by nonlinear least-square iteration with the directly identified harmonic parameters as initial values. Studied the effect of different types of noise on the accuracy of identified parameters, and pointed out the serious effect of the noise which make signal offset on the identification accuracy of nonlinear harmonic components, and this type of noise could lead to the invalid results.
6. Using the nonlinear MIAF and the4th order Runge-Kutta algorithm, performed the nonlinear aerodynamic stability analysis under special conditions, and found that the three types of motion mode including the convergence, the divergence and the large identical-amplitude oscillation could occur at the post-flutter status of long span bridges. Discussed the influence of different parameters in the nonlinear aerodynamic differential equation on motion type and the nonlinear aerodynamic stability, and also discussed the influence of turbulent flow on the nonlinear aerodynamic stability in brief. In addition, based on the features of nonlinear MIAF, interpreted the "hard flutter" and "soft flutter" phenomena in long span bridges.
7. Discussed the outlook of research direction of nonlinear aerodynamics.
1.回顾了大跨度桥梁抗风研究的发展,总结了线性与非线性气动力的研究现状。
2.基于平衡位置的Taylor展开,推导了单自由度运动和弯扭耦合运动条件下非线性自激气动力的复数和实数表达式,建立了由多个谐波分量所组成的非线性自激气动力模型。
3.采用特殊风洞试验技术,开展了大振幅条件下薄翼和流线型箱梁断面的自激力测试,发现了自激力频谱中存在显著的高次谐波分量,验证了非线性自激力是由多个谐波分量所组成的理论结果。发现了自激气动力中非线性分量的幅值随断面运动振幅的增大而增大,随折算风速的增大而减小的一般性规律。
4.研究了流线型箱梁断面非线性自激气动力的迟滞效应。发现箱梁的气动力矩迟滞曲线在一定条件下也能转变为面积相当的“8字环”,该现象表明气动力矩在一个周期内既做了正功,也做了负功。探讨了大跨度桥梁在大振幅条件下可能出现的运行形式。
5.提出了非线性气动参数的识别方法。该方法采用直接提取的谐波参数为初始值,结合非线性最小二乘迭代算法实现。研究了不同形式的噪声对参数识别精度的影响,并指出致使信号发生偏移的噪声对识别结果有较大影响,将直接导致结果失真或不可用。
6.利用非线性自激气动力和四阶龙格-库塔算法,进行了特定条件下箱梁断面的非线性气动稳定分析,发现大跨度桥梁在“颤振后”状态,可能存在收敛、发散和等幅振动三种运动形式。探讨了非线性气动微分方程中参数的变化对运动形式以及气动稳定性的可能影响；简要探讨了紊流风对气动稳定性的影响；结合气动力的非线性特性,解释了大跨度桥梁的“硬颤振”和“软颤振”现象。
7.展望了非线性气动力今后的研究内容和方向。
This thesis reviewed the research of wind effects on the long span bridge, and summarized the current research on the linear and nonlinear Motion-Induced Aerodynamic Force (MIAF). Firstly, based on Taylor expansion of the equilibrium position, the mathematical model of nonlinear MIAF was developed under harmonic motions. Then, through the special wind tunnel tests, the nonlinear MIAF of thin airfoil and streamline box girder were obtained under the large amplitude oscillation, and the characteristics of nonlinear MIAF and aerodynamic hysteresis of the thin airfoil and streamline box girder were also discussed. In addition, the identification method of nonlinear aerodynamic parameters in the expression was proposed. Finally, the nonlinear aerodynamic analysis has been conducted using the nonlinear MIAF.
The thesis research contains following contents:
1. Reviewed the researches of wind effects on long span bridges, and summarized the current researches on the linear and nonlinear MIAF.
2. Based on Taylor expansion of the equilibrium position, deduced the plural and real expression of nonlinear MIAF under1DOF and2DOF harmonic motions, and established the nonlinear MIAF mathematical model composed of multiple harmonic components.
3. Through the special wind tunnel technology, conducted the tests of nonlinear MIAF of the thin airfoil and streamline box girder under the large amplitude oscillation, and found the remarkable higher harmonic components in the spectrum, which validated the theory that the nonlinear MIAF composed of multiple harmonic components. Discovered that the amplitude of nonlinear components in the MIAF increased with the increase of oscillation amplitude, and decreased with the increase of reduced velocity.
4. Studied the characteristics of nonlinear MIAF and aerodynamic hysteresis, and found the exist of "figure8" loop in the aerodynamic moment hysteresis curve of the streamline box girder, that is, the aerodynamic moment has done not only positive work but also negative work in one period. Then discussed the possible vibration status of long span bridges under the large amplitude oscillation.
5. Proposed the identification method of nonlinear aerodynamic parameters. This method could realized by nonlinear least-square iteration with the directly identified harmonic parameters as initial values. Studied the effect of different types of noise on the accuracy of identified parameters, and pointed out the serious effect of the noise which make signal offset on the identification accuracy of nonlinear harmonic components, and this type of noise could lead to the invalid results.
6. Using the nonlinear MIAF and the4th order Runge-Kutta algorithm, performed the nonlinear aerodynamic stability analysis under special conditions, and found that the three types of motion mode including the convergence, the divergence and the large identical-amplitude oscillation could occur at the post-flutter status of long span bridges. Discussed the influence of different parameters in the nonlinear aerodynamic differential equation on motion type and the nonlinear aerodynamic stability, and also discussed the influence of turbulent flow on the nonlinear aerodynamic stability in brief. In addition, based on the features of nonlinear MIAF, interpreted the "hard flutter" and "soft flutter" phenomena in long span bridges.
7. Discussed the outlook of research direction of nonlinear aerodynamics.
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