缆索承重桥梁动态特性初步分析的动力刚度模型研究  

Dynamic Stiffness Modeling for Preliminary Analysis of Dynamic Properties of Cable-Supported Bridges

作　　者：郭吉平 龙殿君 孙远[2] GUO Jiping;LONG Dianjun;SUN Yuan(Guizhou Communications Construction Group Co.,Ltd.,Guiyang 550001,China;School of Civil and Hydraulic Engineering,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]贵州交通建设集团有限公司,贵州贵阳550001 [2]华中科技大学土木与水利工程学院,湖北武汉430074

出　　处：《世界桥梁》2025年第2期58-65,共8页World Bridges

基　　金：国家重点研发计划项目(2023YFC3805705);国家自然科学基金项目(52278308);贵州省交通运输厅重大科技攻关项目(2024-122-007)。

摘　　要：针对有限元模型、传统解析模型在缆索承重桥梁动态特性初步分析时的复杂性及局限性,提出一种计算简单、适用性广的动力刚度模型。首先,建立模型近似初始状态,利用主缆、主梁的竖向振动微分方程推导出精确单元动力刚度矩阵;再通过影响矩阵模拟吊索、斜拉索等弹性连接,组建缆索承重桥梁的整体动力刚度矩阵,得到动力刚度模型;最后通过求解非线性特征值问题获得该模型的动态特性。采用有限元模型、传统解析模型、本文模型分析某典型三跨悬索桥和自锚式斜拉-悬索协作体系桥算例的动态特性,结果表明:相比于有限元模型的竖向振动模态频率参照值,在悬索桥算例中本文模型的频率误差总体上略低于解析模型,而在斜拉-悬索协作体系桥算例中则显著低于解析模型;本文模型在缆索承重桥梁动态特性初步分析方面,不仅规避了有限元模型中复杂的找形计算,而且该模型基于单元尺度,较基于跨度尺度的传统解析模型的计算适用性更广,可用于缆索承重桥梁的初步设计中。This paper presents a dynamic stiffness modeling that overcomes the complexities and limitations of the finite element modeling and conventional analytical modeling in the preliminary analysis of the dynamic properties of cable-supported bridges.Firstly,an initial equilibrium state of the model is established,and the precise element dynamic stiffness matrices are derived by using the vertical vibration dynamic differentiate equations of the main cable and main girder.The effects of the elastic connections,such as the hangers and stay cables,can be considered by a sort of influential matrices.Subsequently,all the matrices are assembled into a global dynamic stiffness matrix and a model dynamic equation for building up the dynamic stiffness model,and finally,the dynamic properties of the model can be obtained by solving a nonlinear eigenvalue problem.The finite element model,conventional analytical model,and the proposed dynamic stiffness model are applied to analyze a typical three-span suspension bridge and a self-anchored hybrid cable-stayed suspension bridge.The results show that compared with the vertical vibration mode frequencies by finite element modeling(as references),the proposed dynamic stiffness modeling of the suspension bridge reveals a slightly lower error rate than the analytical modeling,but significantly lower error rate in the modeling of the hybrid cable-supported bridge.The proposed dynamic stiffness modeling avoids the complex form-finding calculations in the finite element modeling,which is established based on the element scales,rather than the span scales in the conventional analytical modeling,and is of promising use in the preliminary analysis of cable-supported bridges.

关 键 词：缆索承重桥梁 悬索桥 斜拉-悬索协作体系桥 动态特性 解析模型 动力刚度模型 

分 类 号：U441[建筑科学—桥梁与隧道工程]