带垂度水平索桥耦合面内参数振动

Parametric Vibration of Horizontal Cable with Sag and Deck System

摘要:

考虑拉索垂度，建立了水平索桥系统的面内参数振动运动方程.采用分离变量法描述拉索的横向位移，并取拉索的前两阶模态，用Galerkin方法得到拉索二阶广义坐标运动方程；同时，建立桥面等效质量块的运动微分方程.在此基础上，采用多尺度方法，导出了运动方程的理论解.以南京长江二桥A20 拉索为研究对象对拉索响应进行了数值求解，分析了主要参数对拉索响应的影响,并对理论解进行了验证.

Abstract:

This paper presents parametric vibration of a system of a horizontal cable with sag and a mass block representing a bridge deck section under axial harmonic excitation.The differential equations of the cable and the mass are established.By using the variable separation method to cable’s cross displacement and taking the first two modes of the cable into account,the differential equations governing the motions of the first two generalized coordinates of the cable are derived based on Galerkin method.On the basis of the theoretical model,the theoretical solutions of the differential equations of the cable-deck system are derived with multiple-scale method.Taking Cable A20 of No.2 Nanjing Bridge over Yangtze River as an example,the vibration characteristics of the system is numerically investigated and the validity of the theoretical solutions is tested.