大跨度密频斜拉桥模态耦合抖振MDTMD控制  

Controlling the Modal Coupled Buffeting Response of the Long Span Dense-frequency Cable-stayed Bridge by MDTMD

作　　者：沈正峰 胡兆同[1,2] 李加武[1,2] 薛晓锋[1,2] 高广中 SHEN Zheng-feng;HU Zhao-tong;LI Jia-wu;XUE Xiao-feng;GAO Guang-zhong(School of Highway,Chang’an University,Xi’an 710064,Shaanxi,China;Key Laboratory for Bridge and Tunnel of Shaanxi Province,Chang’an University,Xi’an 710064,Shaanxi,China)

机构地区：[1]长安大学公路学院,陕西西安710064 [2]长安大学陕西省公路桥梁与隧道重点实验室,陕西西安710064

出　　处：《中国公路学报》2019年第10期135-149,共15页China Journal of Highway and Transport

基　　金：国家自然科学基金项目(51978077,51078038,51808052);中央高校基本科研业务费专项资金项目(300102219531)

摘　　要：为了对大跨度密频斜拉桥抖振进行控制,基于虚功原理推导出以广义相对位移为未知量的多自由度多模态耦合抖振频域控制方程,总结文献中以位移为最优目标的调谐阻尼器(TMD)最优参数解析解,改进传统双频TMD(DTMD)模型,提出衡量DTMD自身冲程大小的评价标准和采用频响函数峰值分布情况选取控制频宽,对比研究各种参数优化方案和DTMD频率间距对抖振减振效果的影响。研究结果表明,密频斜拉桥抖振响应谱密度峰值的分布特性和一般斜拉桥有明显不同,响应谱在各阶振型频率之间的鞍谷能量不可忽视,各阶振型对主梁不同位置的抖振响应贡献具有差异性。结构阻尼比越小,单个DTMD(SDTMD)减振效果越好,SDTMD控制会出现频响函数能量频移现象。多模态多重调谐质量阻尼器(MDTMD)控制要优于单模态MDTMD控制,改进的DTMD能够在2个方向同时达到良好的减振效果,比传统的DTMD更具优势。分析DTMD频率间距按照均匀分布、二次抛物线分布和频响函数积分等面积分布计算的抖振响应控制效果表明,合理的频率间距能够在相同条件下获得更好的减振效果。单模态和多模态控制得出的结果都表明,Krenk解在综合减振效果上要优于Den Hartog解,采用公路桥梁抗风设计规范(JTG/T 3360-01-2018)中Den Hartog解进行DTMD参数设计时,应增加DTMD的设计阻尼比,且增幅不少于15%。To perform buffeting control on a long-span dense-frequency cable-stayed bridge, this paper derived the multi degrees-of-freedom multimodal coupled buffeting frequency governing equation with generalized relative displacement based on the principle of virtual work. Summarized the tuned mass damper(TMD) optimal parameters with the displacement as the optimal target in the literature, and improved the traditional dual-frequency TMD(DTMD) model. The paper proposed an evaluation standard for the stroke of the DTMD and a method for selecting the control bandwidth using the peak distribution of the frequency response function. Comparative studies were conducted on the effects of various parameter optimization schemes and DTMD frequency spacing on buffeting vibration reduction. The research results show that the distribution characteristics of the buffeting spectral density of the dense-frequency cable-stayed bridge are different from those of the general cable-stayed bridge. The saddle-valley energy of the response spectrum between the various modal frequencies cannot be ignored. Each mode shape has a different contribution to the buffeting response of different positions of the main beam. The lower the structure damping ratio, the better the vibration reduction effect under the single DTMD(SDTMD) condition. The energy frequency shift phenomenon of the frequency response function will appear in the SDTMD control. The comparative analysis results show that the multimodal multiple tuned mass damper(MDTMD) control is superior to the single-mode MDTMD control. The improved DTMD achieves good vibration reduction at the same time in two degrees-of-freedom, which is more advantageous than the traditional DTMD. According to the uniform distribution, quadratic parabola distribution, and equal area of the frequency response function integral, the effect of the DTMD frequency spacing on the buffeting vibration reduction effect are discussed. The results show that reasonable frequency spacing has a better vibration reduction effec

关 键 词：桥梁工程 密频斜拉桥 多模态抖振控制 MDTMD 频率间距 控制频宽 最优参数 

分 类 号：U441.3[建筑科学—桥梁与隧道工程]