斜拉桥多索-浅拱-弹性约束模型及面内自由振动

苏潇阳 康厚军 皮梓豪 丛云跃

摘要：考虑斜拉桥的初始构型和支座刚度，建立了竖向弹性约束下的多索-浅拱动力学模型.首先基于索和浅拱的经典动力学方程，将浅拱在索-拱耦合处分段，推导了竖向弹性约束多索-浅拱的面内自由振动理论.然后采用分离变量法对其面内特征值问题进行了求解.同时以双索-浅拱模型为例，建立了相应的有限元模型，并将论文方法算出的频率和模态与有限元结果进行对比，从而验证了论文方法和模型的正确性.最后，对竖向弹性约束双索-浅拱的动力学特性进行了系统的参数化分析.结果表明：竖向刚度对系统的动力学特性有着明显的影响.

关键词：多索浅拱；动力学模型；弹性约束；自由振动；特征值

中图分类号：O343.9文献标志码：A

基金项目：国家自然科学基金资助项目（11972151，11872176），National Natural Science Foundation of China（11972151，11872176）

Elastically Constrained Multi-cable-stayed Shallow-arch Model in Cable-stayed Bridge and Its in-plane Free Vibration Research

SU Xiaoyang，KANG Houjun，PI Zihao，CONG Yunyue

（College of Civil Engineering，Hunan University，Changsha 410082，China）

Abstract：Considering the initial configuration and support stiffness of cable-stayed bridge，the multi-cablestayed shallow-arch model with vertical elastic constraints is established. Firstly，based on the classical dynamics e-quations of the cable and shallow arch，the theory of in-plane free vibration of the model is deduced by dividing the shallow arch into several segments at the cable-arch coupling points. Then，the double-cable-stayed shallow-arch model is taken as an example and its in-plane eigenvalue problem is solved by separation-of-variable method. At the same time，taking the double-cable-shallow arch model as an example，the corresponding finite element model is es-tablished. The frequencies and mode shapes calculated by the present method are compared with those obtained by fi-nite element method，which verifies the correctness of the method and model in this paper. Finally，a systematic para-metric analysis on the dynamics properties of the model is conducted. It is shown that the vertical stiffness has a sig-nificant effect on the dynamics properties of the system.

Key words：multi-cable-stayed shallow arch；dynamic model；elastic constraints；free vibration；eigenvalue

斜拉橋由于受力性能好、抗震性能强、造型优美及优越的跨越能力在大跨度桥梁中占有十分重要的地位.但由于斜拉桥跨度的不断增大以及新材料的不断应用，结构也变得更轻更柔，其动力学问题也就更为突出.因此，国内外学者对斜拉桥的动力学特性进行了大量研究. Gattulli等[1]通过经典变分公式，建立了斜拉桥索-梁结构横向动力学运动控制方程，并对其特征值问题进行了参数分析.本课题组[2-5]采用传递矩阵法对斜拉梁、双索梁结构的面内振动问题进行了详细的分析.通过考虑斜拉桥中桥塔的振动，提出了多梁离散弹簧动……