大跨人行过街天桥利用MTMD减振控制的理论分析
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摘要
大跨人行天桥的自振频率通常比较低,与人行走时的频率接近,因此行人通过天桥时容易产生竖向共振,影响天桥的正常使用。本文研究多重调谐质量阻尼(MTMD)系统对大跨人行过街天桥竖向振动的控制作用,首先建立起天桥-MTMD系统的分析模型,推导出系统的传递函数及动力放大系数的数学表达式,继而分析了TMD的数量、阻尼比和频带宽等参数对结构的动力放大系数的影响,为实际工程结构设计MTMD减振系统时提供参考。以沈阳某大跨人行天桥为例,进行MTMD优化设置后,能有效减小天桥的受迫振动和自由振动,从而将振动控制在人体的舒适度范围之内。
The lowest natural frequencies of short span pedestrian bridges are usually sufficiently high that they are not susceptible to human-induced vibrations.As spans increase,their lowest natural frequencies become lower and human-induced vibrations become a concern.The lowest frequencies of large-span pedestrian bridges are generally near to the one of walking people,which can result in the resonance of the bridge.It is not economical to avoid the resonance by adjusting the frequency of pedestrian bridge. However,the inclusion of vibration absorbers in pedestrian bridges can be a successful method of mitigating the effects of vertical responses.Multiple Tuned Mass Damper(MTMD) is a kind of dynamic absorber group that consists of a large number of small oscillators with distributed frequencies and damping or mass.In this paper,the control performance of MTMD for the vertical vibration of pedestrian bridges is studied.The mathematical model of a pedestrian bridge with MTMD is established and the transfer function and dynamic magnification factor(DMF) for the control system are derived.The parameters which may affect the DMF,including the numbers of TMD,the damping ratio of MTMD and the band of frequency ratios for MTMD,are analyzed.The analytical results can provide suggestions for the design of MTMD control of pedestrian bridges.The parameters of MTMD are optimized for a large-span pedestrian bridge in Shenyang City.The numerical results indicate that MTMD can effectively reduce the vibration of pedestrian bridge to the acceptable range.
The lowest natural frequencies of short span pedestrian bridges are usually sufficiently high that they are not susceptible to human-induced vibrations.As spans increase,their lowest natural frequencies become lower and human-induced vibrations become a concern.The lowest frequencies of large-span pedestrian bridges are generally near to the one of walking people,which can result in the resonance of the bridge.It is not economical to avoid the resonance by adjusting the frequency of pedestrian bridge. However,the inclusion of vibration absorbers in pedestrian bridges can be a successful method of mitigating the effects of vertical responses.Multiple Tuned Mass Damper(MTMD) is a kind of dynamic absorber group that consists of a large number of small oscillators with distributed frequencies and damping or mass.In this paper,the control performance of MTMD for the vertical vibration of pedestrian bridges is studied.The mathematical model of a pedestrian bridge with MTMD is established and the transfer function and dynamic magnification factor(DMF) for the control system are derived.The parameters which may affect the DMF,including the numbers of TMD,the damping ratio of MTMD and the band of frequency ratios for MTMD,are analyzed.The analytical results can provide suggestions for the design of MTMD control of pedestrian bridges.The parameters of MTMD are optimized for a large-span pedestrian bridge in Shenyang City.The numerical results indicate that MTMD can effectively reduce the vibration of pedestrian bridge to the acceptable range.
引文
[1]叶正强,李爱群,丁幼亮,等.某大跨人行天桥的消能减振设计(一)[J].特种结构,2003,20(1):68-70.Ye Z Q,Li A Q,Ding Y L,et al.The vibrationenergy dissipation design of a pedestrian bridge(1)[J].Special Structures,2003,20(1):68-70.
[2]丁幼亮,李爱群,叶正强,等.某大跨人行天桥的消能减振设计(二)[J].特种结构,2003,20(1):71-73.Ding Y L,Li A Q,Ye Z Q,et al.The vibrationenergy dissipation design of a pedestrian bridge(2)[J].Special Structures,2003,20(1):71-73.
[3]李宏男.结构振动控制实践的新进展[J].世界地震工程,1995,11(2):34-39.Li H N.New progress on applications of structuralvibration control[J].World Earthquake Engineering,1995,11(2):34-39.
[4]Yamaguchi H,Harnpornchai N.Fundamentalcharacteristics of multiple tuned mass dampers forsuppressing harmonically forced oscillations[J].Earthquake Engineering and Structural Dynamics,1993,22(2):51-62.
[5]李春祥,熊学玉.结构MTMD地震反应控制最优控制研究[J].振动与冲击,1999,18(1):63-66.Li C X,Xiong X Y.Research on MTMD optimalparameters to suppress seismic response of structures[J].Journal of Vibration and Shock,1999,18(1):63-66
[6]克拉夫R W,彭津J.结构动力学[M].北京:科学出版社,1981.Clough R W,Penzien J.Dynamics of Structures[M].Beijing:Science Press,1981.
[7]Poovarodom N,Kanchanosot S,Warnitchai P.Application of non-linear multiple tuned mass dampersto suppress man-induced vibrations of a pedestrianbridge[J].Earthquake Engineering and StructuralDynamics,2003,32(7):1117-1131.
[8]Britsh Standards Institution(BSI)BS5400-1978.Vibration Serviceability Requirements for Foot andCycle Track Bridges[S].
[2]丁幼亮,李爱群,叶正强,等.某大跨人行天桥的消能减振设计(二)[J].特种结构,2003,20(1):71-73.Ding Y L,Li A Q,Ye Z Q,et al.The vibrationenergy dissipation design of a pedestrian bridge(2)[J].Special Structures,2003,20(1):71-73.
[3]李宏男.结构振动控制实践的新进展[J].世界地震工程,1995,11(2):34-39.Li H N.New progress on applications of structuralvibration control[J].World Earthquake Engineering,1995,11(2):34-39.
[4]Yamaguchi H,Harnpornchai N.Fundamentalcharacteristics of multiple tuned mass dampers forsuppressing harmonically forced oscillations[J].Earthquake Engineering and Structural Dynamics,1993,22(2):51-62.
[5]李春祥,熊学玉.结构MTMD地震反应控制最优控制研究[J].振动与冲击,1999,18(1):63-66.Li C X,Xiong X Y.Research on MTMD optimalparameters to suppress seismic response of structures[J].Journal of Vibration and Shock,1999,18(1):63-66
[6]克拉夫R W,彭津J.结构动力学[M].北京:科学出版社,1981.Clough R W,Penzien J.Dynamics of Structures[M].Beijing:Science Press,1981.
[7]Poovarodom N,Kanchanosot S,Warnitchai P.Application of non-linear multiple tuned mass dampersto suppress man-induced vibrations of a pedestrianbridge[J].Earthquake Engineering and StructuralDynamics,2003,32(7):1117-1131.
[8]Britsh Standards Institution(BSI)BS5400-1978.Vibration Serviceability Requirements for Foot andCycle Track Bridges[S].
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