基于辐射波浪理论的圆形桥墩动水压力表达式的简化研究
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摘要
为了解决基于辐射波浪理论的圆形桥墩外域水动水压力表达式极其繁冗、难以计算的问题,对动水压力的影响要素如自由表面波、附加阻尼、附加质量进行了研究,通过数学分析、曲线拟合的方法提出了圆形桥墩外域水动水压力的简化表达式。研究结果表明:自由表面波对附加质量、附加阻尼的影响很小,附加阻尼本身也很小,可不考虑自由表面波以及附加阻尼的影响;刚体运动附加质量近似等于弹性振动附加质量,可用易于计算的刚体运动附加质量替代难以计算的弹性振动附加质量。实际深水桥梁在不同地震波作用下的地震响应计算结果表明,简化表达式具有很高的精度和计算效率。
The expressions of hydrodynamic pressure of circular piers caused by outer water based on the radiation wave theory are too complicated to be applied in practice,hence it is necessary to make simplification.The influencing factors of hydrodynamic pressure such as free-surface wave,added damping and added mass were studied,and the simplified expressions were then proposed by the ways of mathematical analysis and curve fitting.The results show that(1) free-surface wave has little effect on added mass and added damping,as added damping itself is a small one,so both of added clamping and free-surface wave can be ignored;(2) added mass caused by rigid motion almost has the same value as the one caused by elastic vibration,so the latter can be substituted by the former which is easier to be calculated.The calculation results of practical deep-water piers under different kinds of seismic wave show that the simplified expressions are efficient and exact enough for practical application.
The expressions of hydrodynamic pressure of circular piers caused by outer water based on the radiation wave theory are too complicated to be applied in practice,hence it is necessary to make simplification.The influencing factors of hydrodynamic pressure such as free-surface wave,added damping and added mass were studied,and the simplified expressions were then proposed by the ways of mathematical analysis and curve fitting.The results show that(1) free-surface wave has little effect on added mass and added damping,as added damping itself is a small one,so both of added clamping and free-surface wave can be ignored;(2) added mass caused by rigid motion almost has the same value as the one caused by elastic vibration,so the latter can be substituted by the former which is easier to be calculated.The calculation results of practical deep-water piers under different kinds of seismic wave show that the simplified expressions are efficient and exact enough for practical application.
引文
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[13]李悦,王克海,李茜,等.动水对深水大跨刚构桥地震响应影响[J].公路交通科技,2011,28(12):76-81.LI Yue,WANG Kehai,LI Xi,et al.Effect ofHydrodynamic Force on Long-span Deep-water RigidFrame Bridge in Earthquake[J].Journal of Highway andTransportation Research and Development,2011,28(12):76-81.
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[15]毕家驹.近海力学导论[M].上海:同济大学出版社,1989.BI Jiaju.Introduction of Offshore Mechanics[M].Shanghai:Tongji University Press,1989.
[16]刘颖.圆柱函数[M].北京:国防工业出版社,1983.LIU Ying.Cylindrical Functions[M].Beijing:NationalDefense Industry Press,1983.
[2]JTJ044—89,公路工程抗震设计规范[S].JTJ044—89,Specifications of Earthquake ResistantDesign for Highway Engineering[S].
[3]GB50111—2006,铁路工程抗震设计规范[S].GB50111—2006,Code for Seismic Design of RailwayEngineering[S].
[4]JTG/TB02-01—2008,公路桥梁抗震设计细则[S].JTG/TB02-01—2008,Guidelines for Seismic Design ofHighway Bridges[S].
[5]WESTERGARRD H M.Water Pressures on Dams duringEarthquakes[J].TransPortation,ASCE,1933,98(2):418-433.
[6]LIAW C Y,CHOPRA A K.Dynamic of TowersSurrounded by Water[J].Earthquake Engineering andStructural Dynamics,1974,3(1):33-497
[7]ZIENKIEWIEZ O C.The Finite Element Method[M].London:MeGraw-Hill,Inc.,1977.
[8]赖伟.地震和波浪作用下深水桥梁的动力响应研究[D].上海:同济大学,2005.LAI Wei.Study on Dynamic Response of Deep-waterBridge under Earthquake and Wave[D].Shanghai:Tongji University,2005.
[9]NITIKITPAIBOON C,BATHE K J.An ArbitraryLagarangian-Eulerian Velocity Potential Formulation forFluid-structure Interaction[J].Computers andStructures,1993,47(4/5):871-891.
[10]LIU W K,CHANG H G.A Method For Fluid StructureInteraction[J].Computers and Structures,1985,20(1/2/3):311-320.
[11]CHEN H C,TAYLOR R L.Vibration Analysis of Fluid-solid Systems Using a Finite Element DisplacementFormulation[J].International Journal for NumericalMethods in Engineering,1990,29(4):683-698.
[12]杨万理,李乔.地震作用下桥墩非竖直棱面动水应力分析[J].土木工程学报,2010,43(增1):72-76.YANG Wanli,LI Qiao.Hydrodynamic Stress on Non-vertical Surface of Pier under Earthquakes[J].ChinaCivil Engineering Journal,2010,43(S1):72-76.
[13]李悦,王克海,李茜,等.动水对深水大跨刚构桥地震响应影响[J].公路交通科技,2011,28(12):76-81.LI Yue,WANG Kehai,LI Xi,et al.Effect ofHydrodynamic Force on Long-span Deep-water RigidFrame Bridge in Earthquake[J].Journal of Highway andTransportation Research and Development,2011,28(12):76-81.
[14]张海龙,张鹏,黄鹏.深水桥梁结构的地震反应分析[J].公路交通科技,2007,24(9):83-86.ZHANG Hailong,ZHANG Peng,HUANG Peng.Earthquake Response of Deep Water Bridge Structure[J].Journal of Highway and Transportation Research andDevelopment,2007,24(9):83-86.
[15]毕家驹.近海力学导论[M].上海:同济大学出版社,1989.BI Jiaju.Introduction of Offshore Mechanics[M].Shanghai:Tongji University Press,1989.
[16]刘颖.圆柱函数[M].北京:国防工业出版社,1983.LIU Ying.Cylindrical Functions[M].Beijing:NationalDefense Industry Press,1983.
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