WALKING COMFORT ANALYSIS AND VIBRATION CONTROL OF BRIDGE WITH CURVED BEAM AND INCLINED ARCH
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摘要: 该文以首座跨越珠江的斜拱曲梁人行景观桥——广州海心桥为研究对象，系统开展其人致振动舒适度与减振控制研究。海心桥采用拱肋外倾10°的斜拱曲梁固结体系，其主拱跨度为198 m，矢跨比约为1/3.5。主桥跨中桥面宽15 m，桥面由圆弧型快、慢行道组成。由于桥梁处于高密度人群区，且结构体系柔度大、受力复杂，人行舒适度问题很突出。为此，该文建立精细化3D有限元模型，通过特征值分析确定人振动荷载敏感频率范围，判别步行力敏感模态阶数，构建对应的步行力荷载。通过时域分析法获得对应的峰值加速度阈值以及舒适度指标完成了人行舒适度评价。提出了安装质量调谐阻尼器以提高桥梁舒适度等级的减振方案，并对阻尼器的安装位置、阻尼、刚度和质量进行了优化设计，有效提高了桥梁的人行舒适度。该文研究结果可为同类型桥梁的人行桥舒适度评价提供参考。Abstract: Takes the first footbridge with curved beam and inclined arch across the Pearl River, Guangzhou Haixin Bridge, as the research object, and systematically studies its human-induced vibration comfort and vibration control. The main arch span is 198 m with a sagittal-to-span ratio of 1/3.5. The bridge deck is 15 m wide in the middle of the span, and the bridge deck consists of circular fast and slow lanes. As the bridge is located in the high-density crowd area, and the structural system is flexible and complex in force, the problem of pedestrian comfort is prominent. A refined 3D finite element model is established to determine the sensitive frequency range of human-induced load through eigenvalue analysis, so that to find the modes sensitive to walking force and construct the corresponding expressions of walking forces. The evaluation of pedestrian comfort is completed by obtaining the corresponding peak acceleration threshold and comfort index through time domain analysis. A damping scheme is proposed to install tuned mass dampers to improve the comfort level of the bridge, and the installation position, damping, stiffness and mass of the dampers are optimized to improve the pedestrian comfort of the bridge effectively. The results of this paper can provide a reference for the evaluation of comfort level of pedestrian bridges of the same type.
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表 1 桥梁前14阶模态动力特性
Table 1. First 14th order modal dynamic properties of the bridge
模态 频率/Hz 振型描述 主桥 拱肋 1 0.538 正对称竖弯 正对称侧弯 2 0.712 反对称竖弯 反对称竖弯 3 0.927 正对称竖弯+扭转 正对称竖弯 4 1.277 反对称竖弯+侧弯 反对称竖弯 5 1.760 反对称竖弯 反对称竖弯 6 1.764 正对称竖弯+扭转 正对称竖弯 7 2.039 反对称竖弯+侧弯 反对称竖弯 8 2.072 正对称竖弯+侧弯 正对称侧弯 9 2.141 正对称竖弯 正对称竖弯 10 2.440 正对称竖弯 正对称竖弯+扭转 11 2.714 正对称竖弯+扭转 正对称竖弯+扭转 12 2.745 正对称竖弯+扭转 正对称竖弯+扭转 13 2.786 正对称竖弯+扭转 正对称侧弯+扭转 14 2.950 反对称竖弯+扭转 反对称侧弯+扭转 
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舒适度等级 舒适度 竖向加速度限值 横向加速度限值 CL1 最好 <0.5 m/s2 <0.1 m/s2 CL2 中等 0.5 m/s2~1.0 m/s2 0.1 m/s2~0.3 m/s2 CL3 最低限度 1.0 m/s2~2.5 m/s2 0.3 m/s2~0.8 m/s2 CL4 不可接受 >2.5 m/s2 >0.8 m/s2
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舒适度等级 舒适度 竖向加速度限值 横向加速度限值 CL1 最好 [0, 0.25f 0.78) [0, 0.1) CL2 合格 [0.25f 0.78, min(0.5f 0.5, 0.7)) [0.1, 0.15f 0.5) CL3 不合格 [min(0.5f 0.5, 0.7), ∞) [0.15f 0.5, ∞)
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模态号 0.5 人/m2 1.0 人/m2 1.5 人/m2 4.6 人/m2 1 0.002 0.004 0.005 0.008 2 0.001 0.002 0.002 0.003 3 0.006 0.015 0.018 0.032 4 0.002 0.006 0.007 0.012 5 0.091 0.218 0.268 0.468 6 0.114 0.273 0.336 0.587 7 0.068 0.163 0.200 0.349 8 0.145 0.348 0.427 0.748 9 0.230 0.553 0.679 1.188 10 0.326 0.784 0.962 1.684 11 0.154 0.371 0.455 0.796 12 0.151 0.364 0.447 0.783 13 0.088 0.211 0.259 0.454 14 0.005 0.012 0.014 0.025
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模态号 0.5 人/m2 1.0 人/m2 1.5 人/m2 1 0.002 0.006 0.008 2 0.001 0.002 0.002 3 0.008 0.025 0.031 4 0.003 0.009 0.011 5 0.115 0.363 0.446 6 0.144 0.455 0.559 7 0.086 0.272 0.333 8 0.184 0.580 0.712 9 0.231 0.730 0.896
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表 6 TMD减振控制方案
Table 6. Vibration damping control solution
TMD类型 控制方向 质量比μ 总重/t 阻尼比 频率/Hz 4 竖向 0.0031 2.25 0.020 1.275 5 竖向 0.0018 1.65 0.013 1.757 6 竖向 0.0018 1.65 0.025 1.761 7 竖向 0.0032 2.40 0.027 2.033 8 竖向 0.0117 3.30 0.071 2.049 9 竖向 0.0185 3.30 0.026 2.102
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峰值加速度模态号 1.0 人/m2 1.5 人/m2 4.6 人/m2 控制前 控制后 舒适度等级 控制前 控制后 舒适度等级 控制前 控制后 舒适度等级 4 0.006 0.005 CL1 0.007 0.006 CL1 0.012 0.011 CL1 5 0.218 0.189 CL1 0.268 0.232 CL1 0.468 0.407 CL2 6 0.273 0.151 CL1 0.336 0.185 CL1 0.587 0.324 CL1 7 0.163 0.153 CL1 0.200 0.188 CL1 0.349 0.329 CL1 8 0.348 0.267 CL1 0.427 0.327 CL1 0.748 0.573 CL2 9 0.553 0.371 CL1 0.679 0.456 CL2 1.188 0.798 CL3 10 0.784 0.249 CL1 0.962 0.305 CL1 1.684 0.534 CL2 11 0.371 0.200 CL1 0.455 0.245 CL1 0.796 0.429 CL1 12 0.364 0.299 CL1 0.447 0.367 CL1 0.783 0.643 CL2 13 0.211 0.138 CL1 0.259 0.170 CL1 0.454 0.297 CL1 14 0.012 0.009 CL1 0.014 0.011 CL1 0.025 0.020 CL1
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峰值加速度模态号 1.0 人/m2 1.5 人/m2 控制前 控制后 舒适度等级 控制前 控制后 舒适度等级 4 0.009 0.008 CL1 0.011 0.011 CL1 5 0.363 0.279 CL1 0.446 0.343 CL1 6 0.455 0.195 CL1 0.559 0.239 CL1 7 0.163 0.237 CL1 0.333 0.292 CL1 8 0.580 0.364 CL1 0.712 0.447 CL1 14 0.730 0.376 CL1 0.896 0.462 CL1
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