摘要
桥梁技术的突飞猛进使得桥梁的跨越能力不断增强,导致桥梁的刚度不断下降,体现出柔性结构特征。1940年Tacoma大桥的垮塌使得风对桥梁结构的作用走进桥梁工程技术人员的视野,众多学者对桥梁风致振动进行了相关研究,基本上得到了各种风致振动机理。时至今日,风致振动对大跨度桥梁的影响无论是在建设阶段还是在运营阶段都已不容忽视。同时,风致振动也是限制桥梁跨度进一步增加的重要制约因素。
本文从风致振动以及控制的研究现状出发,在总结和吸收国内外前人研究成果的基础上,对大跨度桥梁的风致振动以及被动控制加以研究,给出了大跨度桥梁风致振动的频域分析方法和时域分析方法,并使用多种TMD装置对风致振动的被动控制的原理、效果以及参数加以研究,且均编制程序加以实现。本文的主要研究内容包括:
(1)分析了桥梁结构在非线性静力荷载作用下桥梁成桥状态。介绍了悬索桥成桥状态分析的解析法和有限元法、斜拉桥成桥状态和索力优化,分析了大跨度桥梁静风稳定问题。利用增量与内外两重迭代法分别计算了两座桥梁的静风失稳的临界风速,以此静力计算结果作为模态分析的基础。
(2)分析了频域范围内桥梁结构的颤振。详细介绍以有限模态为基础的多种多模态分析方法中的多模态颤振自动分析法,并以具有理想平板截面的简支梁和某在建长江公路悬索桥为例,使用该方法分析了颤振发生的规律和形态。
(3)分析了频域范围内桥梁结构的抖振。利用计算速度较快的虚拟激励法(PEM)对大跨度桥梁进行了抖振分析过程加以推导,在其中使用更为精确的桥梁结构节点等效气动抖振力公式,并与较为精确的大跨度桥梁抖振分析的CQC方法进行比较。以具有理想平板截面的简支梁和某在建长江公路悬索桥作为数值算例进行了验证分析。
(4)分析了时域范围内桥梁结构的风致振动问题。结合大跨度桥梁的结构非线性静力计算结果,分析大跨度桥梁的颤振以及颤抖振在时域内的分析手法。介绍了时域内自激力和脉动风速的模拟方法。对原结构的有限元模型叠加自激力生成的气动刚度、阻尼和质量,将自激力中的时间历程项和抖振力作为外部荷载加入有限元模型。使用ANSYS实现了颤抖振统一时程分析。
(5)利用TMD研究了大跨度桥梁的被动控制问题。结合风致振动的频域计算结果,分析大跨度桥梁的颤振以及颤抖振的被动控制方法,研究了被动控制参数的设定问题。以TMD为代表,介绍了被动控制的基本理论,推导了STMD、DTMD这两种TMD设备的控制原理以及与结构共同运动的动力微分方程。研究大跨度桥梁颤振和考虑自激力的抖振的TMD控制问题,并分别以STMD、DTMD为基础分别计算了具有理想平板截面的简支梁和某在建长江公路悬索桥在TMD装置作用下TMD的颤振控制效率和颤抖振控制效率,并对TMD的参数的取值做了分析研究。
With the rapid development of bridge technology, the span ability of the bridge is continuously enhanced, and the stiffness of the bridge is decreasing, reflecting the flexible structure. The wind effect on the bridge goes into the vision of engineers and technicians since the collapse of Tacoma Bridge in 1940. After that, the wind-induced vibration of bridge is studied densely, and various basic wind-induced vibration mechanisms have been put forward. At present, the influence of vibration to the long span bridge induced by the wind cannot be neglected whether in construction phase or in operation stage. Meanwhile, the vibration of bridge induced by wind is also an important factor restraining the lengthening of the bridge span.
From the research status quo of the wind-induced vibration and its control, the paper studies the wind-induced vibration and passive control of a long span bridge, on the basis of the predecessors' achievements at home and abroad. The paper puts forward the frequency domain and the time domain of the wind-induced vibration of long span bridges, and uses a variety of TMD devices to study the theories, effects and parameters of the passive control, and all these are programming realization. The main research contents include:
(1) Analyzing the completion state of the bridge structure under the effect of a nonlinear static load. The paper introduces the analytical method and finite element method of the completion state of the suspension bridge, the completion state and cable force optimization of cable-stayed bridge, and the problem on the aerostatics stability of long-span bridges. It also has calculated the critical wind speeds in static instability of the two bridges, using the internal and external incremental double method .These are the foundation of modal analysis.
(2) Analyzing the flutter of bridge structure in frequency domain. The multi-mode flutter automatic analysis method, one of the multi-mode analysis methods which are based on the finitude modes, is introduced detailed and used to analyze the rules and patterns of the flutter of the simple supported thin airfoil beam (SSTAB) and a suspension bridge across the Yangtze River being built.
(3) Analyzing the buffeting of bridge structure in frequency domain. The paper uses the pseudo-excitation method (PEM), a method with a fast calculating speed, to deduce the buffeting of the long-span bridge. During the deduction, the paper uses more accurate bridge structure node equivalent aerodynamic force formula, and compares the method with the CQC method. At last, taking SSTAB and the erecting suspension bridge across the Yangtze River as the numerical example, the paper also does a validating analysis.
(4) Analyzing the wind-induced vibration in time domain. Combining with the structure nonlinearity static result, the paper analyzes the flutter and buffeting calculation method in time domain. The paper also introduces the simulation method of self-excited force and turbulence wind velocity in the time domain, adds the aerodynamic stiffness, damper and mass on the original finite element model, uses the time history term of the self-excited force and buffeting force as applied force on the FEM model and realizes the combined flutter and buffeting analysis in time domain by using ANSYS.
(5) Studying the passive control problem of the long-span bridge by the TMD. Combining with the calculated results in frequency domain of the wind-induced vibration, the paper analyzes the passive control method about the flutter and the buffeting in frequency domain, and studies the preferences of passive control parameter. Taking the TMD as an example, it introduces the basic theory of passive control, and deduces the control theory of STMD and DTMD and dynamic differential equation of TMD-structure. It also studies the TMD control issues of flutter and buffeting considering the self-excited force, calculates the flutter control efficiencies and buffeting control efficiencies of the SSTAB and the suspension bridge being built across the Yangtze River on the base of the STMD and DTMD individually, and studies the value selection of TMD’s parameter.
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