CFRP索斜拉桥的索-浅拱模型及面内自由振动分析

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。

Cable-stayed Shallow-Arch Modeling and In-plane Free Vibration Analysis of Cable-stayed Bridge with CFRP Cables

According to the mechanical characteristics of cable-stayed bridge and based on the classical dynamic theories of cable and shallow arch as well as the dynamic equilibrium conditions at the joint between them, the in-plane free vibration theory of a cable-stayed bridge was established. Simultaneously, the geometric nonlinearity of shallow arch and cables were considered in the model in order to account for the effects of both deck’s camber and cable’s sag in the practical long-span cable-stayed bridges. First, the shallow arch was divided into several parts according to the coupled joints of cables and deck. Based on this point and using the Hamilton principle, the in-plane free vibration equations and boundary conditions of multiple cable-stayed shallow-arch system were derived. Then, applying the method of separation of variables, the linearized equations and boundary conditions governing the in-plane free vibration of the system were established. Next, taking the double-cable-stayed shallow-arch as an example, the in-plane eigenvalue problem was solved using the proposed theory and method in this paper. At the same time, a finite element model of the double-cable-stayed shallow-arch was established to verify the analytical solutions, and consistent results were obtained. Finally, the analysis of some key parameters of the CFRP bridges was conducted. It can be found that modulating the rise of arch in a certain range can only affect a modal frequency of the system, while others are rarely influenced. The results show that CFRP cables can improve fundamental dynamic properties of the system, i.e., the bridge with CFRP cables can overcome the deterioration caused by stress relaxation of cables. The content of the paper focuses on the in-plane free vibration of multiple cable-stayed shallow-arch system and enriches the study of the mechanical properties of cable-stayed bridge, which can be used to guide the design of this kind of bridge in practice.