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本文针对斜拉桥的受力特点,基于索和浅拱的经典动力学运动方程,结合拉索与浅拱之间的耦合边界条件,并且考虑两者的几何非线性,建立了斜拉桥的多索-浅拱面内自由振动模型。将浅拱分段处理,结合索、浅拱连接处的动态平衡条件,应用分离变量法,建立多索-浅拱模型的面内自由振动理论。以双索浅拱模型为例,求解其特征值问题。同时,建立了相应的有限元模型,有限元计算结果与本文理论分析吻合良好。最后针对CFRP索斜拉桥的关键参数,基于本文的索-浅拱理论,对面内自由振动进一步研究。研究表明:浅拱的矢高在一定范围内变化,仅对某一阶频率产生影响,而其他各阶频率几乎没影响;CFRP拉索能显著改善索-浅拱组合结构的基本动力学特性。
In this paper, according to the mechanical characteristics of cable-stayed bridges, based on the classical dynamic equations of motion for cables and shallow arches, the coupled boundary conditions between cables and shallow arches are considered, and the geometrical nonlinearity of both cables is considered. MODEL OF MOTIONOVER - SHALLOW FREE VIBRATION MODEL. In this paper, the shallow-arch section treatment is combined with the dynamic equilibrium condition of cable and shallow arch connection, and the method of separating variables is used to establish the theory of free vibration in plane of multi-cable-shallow arch model. Taking the double cable shallow arch model as an example, the eigenvalue problem is solved. At the same time, the corresponding finite element model is established, and the result of FEM is in good agreement with the theoretical analysis. Finally, according to the key parameters of cable-stayed bridge with CFRP cable, based on the cable-shallow arch theory, the in-plane free vibration is further studied. The results show that: the sag of shallow arch varies within a certain range, and only affects the frequency of a certain order, while the frequencies of other orders have almost no effect; CFRP cable can significantly improve the basic dynamic characteristics of cable - shallow arch composite structure.