考虑高阶振型效应的大跨度钢桁拱桥瑞利阻尼参数取值研究

Research on Values of Rayleigh Damping Parameters of Long-Span Steel Truss Arch Bridge Considering Higher-Mode Effects

为了解高阶振型效应对大跨度钢桁拱桥地震反应的影响机制,以及在采用直接积分法时构建合适的瑞利阻尼矩阵,以某490 m跨径钢桁拱桥为背景,采用SAP 2000软件建立全桥弹性动力计算模型。针对主拱圈上(下)弦杆轴力、弯矩,研究振型参与质量最大的7阶(第1、4、8、11、13、23、49阶)振型反应与总反应的占比关系,并对构建瑞利阻尼矩阵的特征频率选取方法展开研究。结果表明:主拱圈上、下弦杆拱脚区域的轴力主要由1阶振型(第1阶)控制,由拱脚向拱顶过渡,逐渐转变为由2~4阶振型控制,高阶振型效应显著;同一阶振型对主拱圈上、下弦杆轴力贡献率及分布规律的影响不同;对于复杂钢桁拱桥,采用振动方向上振型参与质量较大的2阶振型特征频率构建瑞利阻尼矩阵可能因高估了高阶振型阻尼比,导致除拱脚区域以外的拱圈弦杆杆件轴力计算结果偏小,结构偏于不安全;采用直接积分法对复杂钢桁拱桥进行地震反应分析时,建议选取多阶控制振型构建相应的瑞利阻尼工况,并对其计算结果取包络用于抗震设计。

This study focuses on the influential mechanism of higher-mode effects on seismic responses of the long-span steel truss arch bridge and how to construct appropriate Rayleigh damping matrix when using direct integration method.Based on a steel truss arch bridge spanning 490 m,an elastic dynamic calculation model was established in SAP 2000.Given the axle forces and bending moments of the upper and lower chords of the arch,the seven modes(1st,4th,8th,11th,13th,23rd,49th)of the largest mass coefficients are analyzed in terms of the ratio of mode reaction to total reaction,and the methods to select characteristic frequencies for the establishment of Rayleigh damping matrix are discussed.As per the analysis,the axle forces in the arch springing zones of the upper and lower chords are controlled mainly by the 1st-mode vibrations,which is transitioned from arch springing to arch crown and gradually changed to be controlled by the 2nd to 4th modes of vibrations,with remarkable higher-mode effects.Vibrations of a particular mode exert different effects on the contribution ratio of axle forces and axle force distribution of the upper and lower chords of main arch.For the complex steel truss arch bridge,the Rayleigh damping matrix built with the 2nd-mode characteristic frequencies that offer relatively large vibration participation mass coefficients along the vibration direction may overestimate the higher-mode damping ratio,thus resulting in smaller calculated axle forces in the truss members besides the arch springing zones,and making the structure to have narrow safety margin.When the direct integration method is used to analyze the seismic responses of the complex steel truss arch bridge,it is recommended to establish the Rayleigh damping conditions by selecting multiple-mode vibrations,and take the envelope of the calculation results for seismic design.