多跨下承式拱桥面内全局动力学理论与自由振动研究

为弥补高维工程结构有限元分析对结构参数优化设计等的局限，本文基于欧拉伯努利梁理论与传递矩阵法，研究大跨度拱桥面内自由振动问题.首先，基于多跨拱桥的刚度分析，建立系统的全局动力学模型.其次，基于传递矩阵法建立系统的全局动力学理论，最后，以一座四跨下承式拱桥的平面力学模型，求解其面内自由振动时的固有频率与振型，并将所得结果与用同样参数建模的有限元分析结果对比，证明本文所建理论对求解该类问题的有效性与精确性.此外，通过整桥各跨矢跨比、吊杆截面面积、拱肋惯性矩等的多组参数组合分析了该系统面内自振频率的分布规律.结果表明：随着拱桥矢高增大，系统固有频率减小，因拱桥质量的快速增加，对整桥面内刚度影响显著；增大吊杆截面面积可在一定程度内增大拱桥的面内刚度，导致系统频率在一定范围内增大，且观察到Veering现象.

Study on in-plane global dynamic theory and free vibration of multi span through arch bridge

To make up for the limitations of high-dimensional engineering structure finite element analysis in structural parameter optimization design, this paper studies the in-plane free vibration of Long-span Arch Bridges Based on Euler Bernoulli beam theory and transfer matrix method. Firstly, based on the stiffness analysis of multi span arch bridge, the global dynamic model of the system is established. Secondly, the global dynamic theory of the system is established based on the transfer matrix method. Finally, the natural frequency and vibration mode of a four span through arch bridge are solved by using the plane mechanical model, and the results are compared with the finite element analysis results modeled with the same parameters, which proves the effectiveness and accuracy of the theory established in this paper for solving this kind of problems. In addition, by changing the rise span ratio of each span of the whole bridge, the sectional area of suspenders and the moment of inertia of arch ribs, the variation trend of the natural vibration frequency in the plane of the system is analyzed. The results show that with the increase of the rise height of the arch bridge, the natural frequency of the system decreases, and the rapid increase of the quality of the arch bridge has a significant impact on the stiffness of the whole bridge deck; Increasing the cross-sectional area of the suspender can increase the in-plane stiffness of the arch bridge to a certain extent, resulting in the increase of the system frequency within a certain range, and the veering phenomenon is observed.