地震作用下密频拱桥Rayleigh阻尼的优化解

为建立频谱密集结构的阻尼矩阵,以地震反应谱理论为基础,基于完全二次组合(CQC)提出了求解Rayleigh阻尼系数的优化分析方法.在此基础上,为实现任意阶模态阻尼比等于精确阻尼的要求,利用Lagrange乘子法进一步建立了求解Rayleigh阻尼系数约束优化方法.以一座斜交曲梁下承式钢结构吊索拱桥为例,讨论优化分析所得Rayleigh阻尼系数的稳定性,比较了不同的优化目标组合、约束条件对优化参考频率和地震反应的影响,以及约束优化解中约束模态的选取问题.数值分析结果表明,与平方和开平方组合(SRSS)相比,CQC组合所得的Rayleigh阻尼系数的地震反应计算误差更小,约束模态应该选取对结构地震反应有显著贡献的第一阶模态.

An optimization solution of Rayleigh damping coefficients on arch bridges with closely-spaced natural frequencies subjected to seismic excitations

An optimization solution of Rayleigh damping coefficients is proposed to construct the damping matrix of structures with closely-spaced natural frequencies based on the seismic response spectrum theory and the complete quadratic combination (CQC) rule. A constrained optimization method is further developed to enforce the arbitrary order mode damping ratio equal to the precise value by Lagrange multiplier method. A curved girder skew through steel suspension arch bridge is analyzed to investigate the characteristics of the proposed method. Firstly, the solution stability of optimal Rayleigh damping coefficients is discussed, Secondly. the effects of the different combinations of optimal objective functions and constraint conditions on optimal reference frequencies and seismic response are compared, and the selection of constraints mode in constrained condition is also discussed. Numerical results show that the seismic response calculation error is smaller while the Rayleigh damping coefficients is obtained from CQC rather than the square root of sum square (SRSS) combination. The constrained mode should be specified as the first order significant mode corresponding to structural seismic responses.