大跨度桥梁颤振及涡激振动主动控制
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摘要
颤振是大跨度桥梁风致振动中最具毁灭性的振动,是桥梁向大跨度发展的制约因素,研究提高大跨度桥梁颤振稳定性的措施,是建造主跨跨径超过2000m的大跨度桥梁必须解决的关键问题。论文在总结国内外大跨度桥梁颤振控制方法的基础上,利用现代控制理论,对大跨度桥梁颤振主动控制的方法进行了研究。涡激振动是由气流绕过桥梁时产生的旋涡脱落而激发起的振动,虽然没有颤振那样危险,但由于涡激振动是桥梁在低风速下容易发生的一种风致振动,因此必须对涡激振动进行控制,论文研究了对大跨度桥梁涡激振动进行主动控制的理论与方法,主要进行了以下工作。
1.回顾了目前大跨度桥梁颤振及涡激振动控制的研究现状,并对各种方法进行了分析与评述；
2.建立了大跨度桥梁颤振AMD主动控制的运动方程,然后将此振动系统的运动方程转化到状态空间里；
3.利用次最优控制理论,研究了对大跨度桥梁颤振进行了主动控制的理论与方法,并以一大跨度悬索桥为例,验证了颤振主动控制方法的有效性；
4.分别基于线性涡激力模型与非线性涡激力模型,在频域和时域里研究了大跨度桥梁涡激振动TMD被动控制的理论,分析了振动系统的频率响应,提出了TMD参数优化的方法,并以一大跨度悬索桥为例,进行了算例验证；
5.基于经验线性涡激力模型,在频域和时域里研究了大跨度桥梁涡激振动AMD主动控制的理论,推导了振动系统的频率响应,基于瞬时最优理论,在状态空间里得到了桥梁涡激振动主动控制力,并进行了主动控制效果的算例验证；
6.基于经验非线性涡激力模型,建立了大跨度桥梁非线性涡激振动主动控制系统的运动方程,利用微分几何理论,对非线性振动系统进行了微分同胚变换,实现了非线性振动系统的部分反馈线性化；
7.通过Lyapunov稳定性理论,得到了非线性主动控制律表达式,求解了非线性振动系统的响应,并通过算例验证了桥梁涡激振动非线性主动控制的有效性；
Flutter is the most destructive wind induced vibration of long-span bridges, which is one of the key factors restricting the development of long-span bridges. As far as the bridge with a main span more than2000m, it is a critical issues to suppress the flutter of bridge.This paper reviews and summarizes the domestic and international research of flutter control for long-span bridge, based on the modern control theory, the flutter active control of long-span bridges was analyzed. Vortex-induced vibration is produced by vortex shedding when airflow around the bridge, although there is no chatter as dangerous as flutter, but this vibration occurs at very low wind speed, it is necessary to control vortex-induced vibration of long-span bridges. In this paper, the theories and methods of active control for vortex-induced vibration of long-span bridges are studied. The main research contents of this thesis are shown below:
1. Theories and methods of control for flutter and vortex-induced vibration of long-span bridges were reviewed and summarized;
2. A two-dimensional model of flutter control for suspension bridge using active mass damper is formulated, the aeroelastic equations of motion of bridge and AMD are derived in time domain, then the motion equations of this dynamic system are transformed into state space model;
3. Based on the suboptimal theory, the method of flutter active control for long-span bridges was put forward, and the active control effectiveness was confirmed by taking a long-span suspension bridge as example;
4. The passive controls for vortex-induced vibration of long-span bridges based on the linear and nonlinear empirical vortex-induced force model were studied in the frequency-domain and time-domain respectively. The frequency response functions of the linear vibration system are analyzed; the method to design optimal TMD parameters is given and verified using a long-span suspension bridge;
5. The active control for vortex-induced vibration of long-span bridges using AMD based on the linear empirical vortex-induced force model was studied in frequency domain and time domain. The frequency response functions of the linear vibration system were derived, by the use of instantaneous optimal theory, active control law of vortex-induced vibration of long-span bridges was obtained in state space, and the efficiency of the method was investigated by a long-span suspension bridge;
6. Based on the nonlinear empirical vortex-induced force model, the aeroelastic equation of motion of nonlinear vibration systems consist of bridge and AMD are derived. Then, the partial feedback linearization model of nonlinear vibration systems was obtained using diffeomorphism transform of differential geometry theory;
7. Nonlinear active control law was established from Lyapunov stability theory, the dynamic responses of the nonlinear vibration system were solved, and the results of example shown that the method of the active control was effective.
1.回顾了目前大跨度桥梁颤振及涡激振动控制的研究现状,并对各种方法进行了分析与评述；
2.建立了大跨度桥梁颤振AMD主动控制的运动方程,然后将此振动系统的运动方程转化到状态空间里；
3.利用次最优控制理论,研究了对大跨度桥梁颤振进行了主动控制的理论与方法,并以一大跨度悬索桥为例,验证了颤振主动控制方法的有效性；
4.分别基于线性涡激力模型与非线性涡激力模型,在频域和时域里研究了大跨度桥梁涡激振动TMD被动控制的理论,分析了振动系统的频率响应,提出了TMD参数优化的方法,并以一大跨度悬索桥为例,进行了算例验证；
5.基于经验线性涡激力模型,在频域和时域里研究了大跨度桥梁涡激振动AMD主动控制的理论,推导了振动系统的频率响应,基于瞬时最优理论,在状态空间里得到了桥梁涡激振动主动控制力,并进行了主动控制效果的算例验证；
6.基于经验非线性涡激力模型,建立了大跨度桥梁非线性涡激振动主动控制系统的运动方程,利用微分几何理论,对非线性振动系统进行了微分同胚变换,实现了非线性振动系统的部分反馈线性化；
7.通过Lyapunov稳定性理论,得到了非线性主动控制律表达式,求解了非线性振动系统的响应,并通过算例验证了桥梁涡激振动非线性主动控制的有效性；
Flutter is the most destructive wind induced vibration of long-span bridges, which is one of the key factors restricting the development of long-span bridges. As far as the bridge with a main span more than2000m, it is a critical issues to suppress the flutter of bridge.This paper reviews and summarizes the domestic and international research of flutter control for long-span bridge, based on the modern control theory, the flutter active control of long-span bridges was analyzed. Vortex-induced vibration is produced by vortex shedding when airflow around the bridge, although there is no chatter as dangerous as flutter, but this vibration occurs at very low wind speed, it is necessary to control vortex-induced vibration of long-span bridges. In this paper, the theories and methods of active control for vortex-induced vibration of long-span bridges are studied. The main research contents of this thesis are shown below:
1. Theories and methods of control for flutter and vortex-induced vibration of long-span bridges were reviewed and summarized;
2. A two-dimensional model of flutter control for suspension bridge using active mass damper is formulated, the aeroelastic equations of motion of bridge and AMD are derived in time domain, then the motion equations of this dynamic system are transformed into state space model;
3. Based on the suboptimal theory, the method of flutter active control for long-span bridges was put forward, and the active control effectiveness was confirmed by taking a long-span suspension bridge as example;
4. The passive controls for vortex-induced vibration of long-span bridges based on the linear and nonlinear empirical vortex-induced force model were studied in the frequency-domain and time-domain respectively. The frequency response functions of the linear vibration system are analyzed; the method to design optimal TMD parameters is given and verified using a long-span suspension bridge;
5. The active control for vortex-induced vibration of long-span bridges using AMD based on the linear empirical vortex-induced force model was studied in frequency domain and time domain. The frequency response functions of the linear vibration system were derived, by the use of instantaneous optimal theory, active control law of vortex-induced vibration of long-span bridges was obtained in state space, and the efficiency of the method was investigated by a long-span suspension bridge;
6. Based on the nonlinear empirical vortex-induced force model, the aeroelastic equation of motion of nonlinear vibration systems consist of bridge and AMD are derived. Then, the partial feedback linearization model of nonlinear vibration systems was obtained using diffeomorphism transform of differential geometry theory;
7. Nonlinear active control law was established from Lyapunov stability theory, the dynamic responses of the nonlinear vibration system were solved, and the results of example shown that the method of the active control was effective.
引文
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