斜拉桥拉索的索—梁相关振动研究

发布时间：2018-05-20 00:13

本文选题：斜拉桥 + 拉索　；参考：《西南交通大学》2015年博士论文

【摘要】：斜拉索具有刚度小、阻尼小、质量小的特点,容易在各种激励作用下发生振动,影响桥梁结构的安全。本文结合拉索非线性振动的理论方法与有限元方法,以实际工程为背景,主要研究了铁路斜拉桥在外部动力荷载作用下索-梁相关振动的特性,为斜拉桥的分析与设计提供参考。第2章,为了研究单根拉索的振动特性,考虑拉索大幅振动各阶模态的耦合效应,推导了有垂度拉索在三维空间中大幅振动的理论方程。使用多尺度方法讨论了拉索振动方程的性质,分析拉索大幅非线性振动的特性。编制计算程序,使用数值方法计算了拉索非线性振动方程,验证了理论方法的分析结果。第3章,建立了基于单元流动坐标系(CR列式)的非线性静力算法与动力时程积分算法,开发了非线性静、动力有限元计算程序,使用ANSYS验证了程序的正确性与可靠性,程序适用于拉索大幅度非线性振动的研究。第4章,根据某实际斜拉桥的拉索参数,使用本文程序建立有限元模型,讨论了拉索垂度、抗弯刚度、大幅振动状态对拉索振动特性的影响,计算拉索在端点位移激励作用下的非线性振动时程,通过和理论方程数值计算结果的对比,验证了理论方程的可靠性与适用性,为开发本文有限元程序的“索动力单元”奠定了理论基础。第5章,定义了本文“索-梁相关振动”的概念,认为其主要包含了拉索的强迫振动与参数振动这两种形式。结合拉索振动的理论方程与有限元方法,开发了“索动力单元”。使用本文程序构建了较为简单的索-梁相关振动有限元模型,用索动力单元模拟斜拉索,通过分析计算结果,总结了结构发生索-梁相关振动时的本质规律,为斜拉桥全桥索-梁相关振动研究建立了关键性的理论与技术基础。第6,7章,讨论了本文使用的车桥耦合振动计算方法。基于拉索非线性振动理论方法、有限元方法、车桥耦合振动算法,使用本文程序,构建了某实际铁路斜拉桥的全桥有限元模型,拉索使用索动力单元模拟。首先,讨论了各个拉索自振频率与全桥自振频率的匹配关系,分析拉索发生共振的可能性；然后,分别讨论了斜拉桥在自由振动、理想外激励作用的情况下发生大幅度索-梁相关振动时的振动特性；根据本文的分析结果,讨论了在列车不同工况的作用下,铁路斜拉桥索-梁相关振动的特性,研究结果表明：对于大跨度铁路斜拉桥,列车在设计速度范围内经过桥梁时,索-梁相关振动导致拉索发生大幅度振动的可能性较小。最后,总结本文研究结果,提出了在斜拉桥设计中的避免索-梁相关振动导致拉索大幅振动的参考原则。
[Abstract]:The cable has the characteristics of low stiffness, small damping and low mass. It is easy to vibrate under various excitations and affect the safety of bridge structure. Based on the theoretical method and finite element method of cable nonlinear vibration, the characteristics of cable-beam related vibration of railway cable-stayed bridge under external dynamic loads are studied in this paper. It provides reference for the analysis and design of cable-stayed bridge. In chapter 2, in order to study the vibration characteristics of single cable, considering the coupling effect of various modes of large amplitude vibration of cable, the theoretical equation of large amplitude vibration of cable with sag is derived in three dimensional space. The properties of cable vibration equation are discussed by using multi-scale method, and the characteristics of large nonlinear vibration of cable are analyzed. The numerical method is used to calculate the nonlinear vibration equation of cable, and the analytical results of the theoretical method are verified. In chapter 3, a nonlinear static algorithm and a dynamic time-history integral algorithm based on the element flow coordinate system are established, and the nonlinear static and dynamic finite element calculation programs are developed. The correctness and reliability of the program are verified by ANSYS. The program is suitable for the study of large amplitude nonlinear vibration of cables. In chapter 4, according to the cable parameters of a practical cable-stayed bridge, the finite element model is established by using the program in this paper, and the effects of cable sag, bending stiffness and large vibration state on the cable vibration characteristics are discussed. The nonlinear vibration time history of the cable subjected to the displacement excitation at the end of the cable is calculated. The reliability and applicability of the theoretical equation are verified by comparing with the numerical results of the theoretical equation. It lays a theoretical foundation for the development of the cable dynamic element of the finite element program in this paper. In chapter 5, the concept of "cable-beam associated vibration" is defined, which mainly includes the forced vibration and parametric vibration of cable. Combined with the theoretical equation of cable vibration and finite element method, the cable dynamic element is developed. A simple finite element model of cable-beam related vibration is constructed by using the program in this paper. The cable dynamic element is used to simulate the cable-stayed cable. By analyzing and calculating the results, the essential law of the cable-beam related vibration is summarized. A key theoretical and technical foundation for the study of cable-beam related vibration of cable-stayed bridge is established. In Chapter 6 and 7, the calculation method of vehicle-bridge coupling vibration used in this paper is discussed. Based on the nonlinear vibration theory, finite element method and vehicle-bridge coupled vibration algorithm, the finite element model of a real cable-stayed railway bridge is constructed by using the program in this paper, and the cable dynamic element is used to simulate the cable. Firstly, the matching relation between the natural vibration frequency of each cable and the natural vibration frequency of the whole bridge is discussed, and the possibility of the cable resonance is analyzed, and then the free vibration of the cable-stayed bridge is discussed respectively. The vibration characteristics of cable-beam related vibration of railway cable-stayed bridge under different working conditions of railway cable-stayed bridge are discussed according to the analysis results of this paper. The results show that, for long-span railway cable-stayed bridge, the possibility of cable vibration caused by cable-beam vibration is small when the train passes through the bridge within the design speed range. Finally, the research results are summarized, and the reference principle of avoiding cable-beam vibration caused by cable-beam vibration in the design of cable-stayed bridge is put forward.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：U441.3;U448.27

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