悬索桥线性液体黏滞阻尼器阻尼系数优化
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摘要
将悬索桥加劲梁纵向运动简化为若干相互独立的单自由度振动系统,采用随机振动理论,利用将地震激励简化为平稳白噪声激励的方法推导了加劲梁纵向运动绝对加速度均方的解析表达式。利用导数求极值的原理,求出了加劲梁纵向运动绝对加速度均方的最小值及其对应的系统最优阻尼比,得到了悬索桥线性液体黏滞阻尼器最优阻尼系数的解析表达式,并以某悬索桥为例,采用动力时程法进行了参数敏感性分析,验证了解析表达式的有效性。分析结果表明:悬索桥线性液体黏滞阻尼器存在理论上的最优阻尼比0.5,其对应的最优阻尼系数使阻尼器的减震效率达到最大值;当阻尼比为0.3时,阻尼器的减震效率达到最优阻尼比的90%;当阻尼比在0.4～0.6之间时,阻尼器的减震效率基本保持在最优阻尼比的99%。综合考虑地震动强度、阻尼器冲程及造价等因素,线性液体黏滞阻尼器的最优阻尼系数可在阻尼比为0.4～0.6对应的范围内适当调整。
The longitudinal vibration of suspension bridge stiffening girder was simplified as some independent single degree of freedom vibration systems.Stochastic vibration theory was used,and earthquake excitation was simplified as stationary white-noise excitation,the analytical expression of absolute acceleration mean square for stiffening girder longitudinal vibration was deduced.According to the principle of derivative extremum,the minimum absolute acceleration mean square and the corresponding system optimum damping ratio were derived,and the analytical expression of optimum damping coefficient for suspension bridge linear fluid viscous damper was got.A suspension bridge was selected as example,parametric sensitivity study was carried out based on dynamic time-historical method,and the reliability of the analytical expression was verified.Analysis result shows that the theoretical optimum damping ratio of suspension bridge linear fluid viscous damper is 0.5,and the efficiency of damper reaches its maximum with the corresponding optimum damping coefficient.When damping ratio is 0.3,damper efficiency is about 90% of optimum damping ratio.When damping ratio is 0.4-0.6,damper efficiency is 99% of optimum damping ratio,so the optimum damping coefficient of linear fluid viscous damper can be adjusted properly in the range according to earthquake intensity,damper stroke and cost.
The longitudinal vibration of suspension bridge stiffening girder was simplified as some independent single degree of freedom vibration systems.Stochastic vibration theory was used,and earthquake excitation was simplified as stationary white-noise excitation,the analytical expression of absolute acceleration mean square for stiffening girder longitudinal vibration was deduced.According to the principle of derivative extremum,the minimum absolute acceleration mean square and the corresponding system optimum damping ratio were derived,and the analytical expression of optimum damping coefficient for suspension bridge linear fluid viscous damper was got.A suspension bridge was selected as example,parametric sensitivity study was carried out based on dynamic time-historical method,and the reliability of the analytical expression was verified.Analysis result shows that the theoretical optimum damping ratio of suspension bridge linear fluid viscous damper is 0.5,and the efficiency of damper reaches its maximum with the corresponding optimum damping coefficient.When damping ratio is 0.3,damper efficiency is about 90% of optimum damping ratio.When damping ratio is 0.4-0.6,damper efficiency is 99% of optimum damping ratio,so the optimum damping coefficient of linear fluid viscous damper can be adjusted properly in the range according to earthquake intensity,damper stroke and cost.
引文
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[12]梁鹏,吴向男,李万恒,等.三塔悬索桥纵向约束体系优化[J].中国公路学报,2011,24(1):59-67.LIANG Peng,WU Xiang-nan,LI Wan-heng,et al.Longitu-dinal constraint system optimization for three-tower suspen-sion bridge[J].China Journal of Highway and Transport,2011,24(1):59-67.(in Chinese)
[13]赵国辉,李宇,刘健新.大跨径悬索桥液体黏滞阻尼器参数敏感性研究[J].中国安全科学学报,2011,21(11):35-40.ZHAO Guo-hui,LI Yu,LIU Jian-xin.Parametric sensitivity study on fluid viscous damper of long span suspension bridge[J].China Safety Science Journal,2011,21(11):35-40.(in Chinese)
[2]李爱群,王浩.大跨悬索桥地震响应控制的阻尼器最优布置方法[J].东南大学学报:自然科学版,2009,39(2):315-319.LI Ai-qun,WANG Hao.Optimal placement method of dampers for seismic control of long-span suspension bridges[J].Journal of Southeast University:Natural Science Edition,2009,39(2):315-319.(in Chinese)
[3]卢桂臣,胡雷挺.西堠门大桥液体粘滞阻尼器参数分析[J].世界桥梁,2005(2):43-45.LU Gui-chen,HU Lei-ting.Analysis of parametric sensitivity of fluid viscous dampers for Xihoumen Bridge[J].World Bridges,2005(2):43-45.(in Chinese)
[4]聂利英,李建中,胡世德,等.任意荷载作用下液体粘滞阻尼器在桥梁工程中减震作用探讨[J].计算力学学报,2007,24(2):197-202.NIE Li-ying,LI Jian-zhong,HU Shi-de,et al.Investigation of decreasing vibration effects of fluid viscous damper in bridge engineering under random loads[J].Chinese Journal of Computational Mechanics,2007,24(2):197-202.(in Chinese)
[5]LIU Wei,TONG Mai,LEE G C.Optimization methodology for damper configuration based on building performance indices[J].Journal of Structural Engineering,2005,131(11):1746-1756.
[6]PEKCAN G,MANDER J B,CHEN S S.Fundamental con-siderations for the design of non-linear viscous dampers[J].Earthquake Engineering and Structural Dynamics,1999,28(11):1405-1425.
[7]LIN W H,CHOPRA A K.Earthquake response of elastic single-degree-of-freedom systems with nonlinear viscoelastic dampers[J].Journal of Engineering Mechanics,2003,129(6):597-606.
[8]MARTINEZ-RODRIGO M,ROMERO M L.An optimum retrofit strategy for moment resisting frames with nonlinear viscous dampers for seismic applications[J].Engineering Structures,2003,25(7):913-925.
[9]MIRANDA E,BERTERO V V.Evaluation of strength reduction factors for earthquake-resistant design[J].Earth-quake Spectra,1994,10(2):357-379.
[10]LEE D,TAYLOR D P.Viscous damper development and future trends[J].The Structural Design of Tall and Special Buildings,2001,10(5):311-320.
[11]MCNAMARA R J,TAYLOR D P.Fluid viscous dampers for high-rise buildings[J].The Structural Design of Tall and Special Buildings,2003,12(2):145-154.
[12]梁鹏,吴向男,李万恒,等.三塔悬索桥纵向约束体系优化[J].中国公路学报,2011,24(1):59-67.LIANG Peng,WU Xiang-nan,LI Wan-heng,et al.Longitu-dinal constraint system optimization for three-tower suspen-sion bridge[J].China Journal of Highway and Transport,2011,24(1):59-67.(in Chinese)
[13]赵国辉,李宇,刘健新.大跨径悬索桥液体黏滞阻尼器参数敏感性研究[J].中国安全科学学报,2011,21(11):35-40.ZHAO Guo-hui,LI Yu,LIU Jian-xin.Parametric sensitivity study on fluid viscous damper of long span suspension bridge[J].China Safety Science Journal,2011,21(11):35-40.(in Chinese)
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