Dynamic Characteristics of Long-span Suspension Bridge with Variability of Stiffness of Expansion Joints
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摘要: 伸缩缝作为大跨度桥梁与引桥之间的重要连接构件，其抗推刚度及可能存在的变异性对主桥及引桥动力特性的影响不可忽略。本文建立了大跨度悬索桥及引桥的有限元模型，采用弹簧单元模拟加劲梁与引桥箱梁之间的伸缩缝，分析伸缩缝刚度对悬索桥及引桥自振特性及其地震响应的影响规律。分析结果表明：伸缩缝刚度对加劲梁的横弯振型、竖弯与纵飘耦合振型的频率有明显的影响；伸缩缝刚度的变化会导致加劲梁与引桥的振型相互耦合，同时这些振型的频率发生相应的突变，当伸缩缝刚度较大时，加劲梁两个竖弯与纵飘的耦合振型解耦成为独立的竖弯和纵飘振型；当引桥与悬索桥加劲梁的纵飘振型发生耦合时，在纵向和竖向地震作用下的悬索桥及引桥的地震响应达到最小。伸缩缝刚度对悬索桥动力特性影响的分析可为悬索桥的模态参数确认、损伤识别、抗震性能分析提供有价值的借鉴。Abstract: As an important connecting component between the long-span bridge and approach bridge, the anti-push rigidity and the possible variability of the expansion joints cannot be neglected for the dynamic characteristics of main bridge and approach bridge. The finite element model of long-span suspension bridge and approach bridge is established in this paper. The spring element is used to simulate the expansion joints between stiffening girder of suspension bridge and box girder of approach bridge, and the influence of stiffness of expansion joints on natural frequency characteristics and seismic response of suspension bridge and approach bridge is analyzed. The results show that:① The stiffness of expansion joints has a significant effect on the frequency of transverse bending modes and coupling mode frequency of vertical bending and longitudinal floating of stiffening girder. ② The change of stiffness of expansion joints may result in the coupling of stiffening girder and approach bridge, and the frequency of these modes may change accordingly. When the stiffness of the expansion joint is large, two coupling mode of vertical bending and longitudinal floating of stiffening girder are decoupled into two independent vertical and longitudinal vibration modes respectively. ③ The seismic response of suspension bridge and approach bridge under the action of longitudinal and vertical earthquakes is minimized when the longitudinal floating mode is coupled between stiffening girder of suspension bridge and approach bridge. The analysis of influence of stiffness of the expansion joints on dynamic characteristics of suspension bridge can provide a valuable reference for the modal parameter identification, damage identification and seismic performance analysis of suspension bridge.
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图 1 悬索桥及引桥的支承体系布置
Figure 1. Arrangement of support system of suspension bridge and approach bridge
图 2 悬索桥有限元模型及伸缩缝模拟
Figure 2. Finite element model of suspension bridge and simulation of expansion joints
图 3 悬索桥加劲梁自振频率与伸缩缝刚度关系曲线
Figure 3. Relationship between natural frequency of stiffening girder and stiffness of expansion joints
图 4 引桥自振频率与伸缩缝刚度关系曲线
Figure 4. Relationship between natural frequency of approach bridge and stiffness of expansion joints
图 6 梁端伸缩缝及阻尼器的最大位移和行程
Figure 6. Maximum displacement and stroke of expansion joint and damper
图 9 加劲梁最大横向弯矩及竖向位移
Figure 9. Maximum transverse bending moment and vertical displacement of stiffening beam
表 1 悬索桥加劲梁及引桥的自振频率
Table 1. Natural frequency of stiffening girder of suspension bridge and approach bridge
部位 阶次 频率/Hz 振型描述 简称 部位 阶次 频率/Hz 振型描述 简称 加劲梁 1 0.069 一阶正对称横弯 LS1 加劲梁 36 0.472（0.4579） 三阶正对称竖弯 VS3 2 0.095 一阶反对称竖弯（左上右下）+纵飘 VA1-1 39 0.504 二阶正对称横弯 LS2 3 0.136 一阶反对称竖弯（左下右上）+纵飘 VA1-2 42 0.535 二阶正对称扭转 TS2 4 0.148（0.1465） 一阶正对称竖弯（跨中向上） VS1-1 43 0.569 四阶反对称竖弯 VA4 5 0.200 一阶正对称竖弯（跨中向下） VS1-2 49 0.677（0.6352） 四阶正对称竖弯 VS4 6 0.210 一阶反对称横弯 LA1 54 0.695 二阶反对称扭转 TA2 7 0.233 二阶反对称竖弯 VA2 60 0.796 五阶反对称竖弯 VA5 14 0.297 一阶正对称扭转 TS1 69 0.852 二阶反对称横弯 LA2 16 0.307（0.3052） 二阶正对称竖弯 VS2 71 0.873 三阶正对称扭转 TS3 23 0.352 一阶反对称扭转 TA1 74 0.927 五阶正对称竖弯 VS5 29 0.383 三阶反对称竖弯 VA3 右引桥 12 0.286 纵飘 左引桥 27 0.374 一阶正对称横弯 18 0.319 一阶正对称横弯 40 0.511 纵飘 47 0.656 一阶反对称横弯 69 0.852 一阶正对称横弯 
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