地震下矩形空心桥墩内部动水力分析
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摘要
针对地震下矩形空心桥墩内部的动水力,提出了一个近似半解析半数值方法。对于弹性桥墩结构,基于线性辐射波浪理论利用特征函数扩展法分别构造了桥墩内部二维流体的弹性振动速度势和刚性运动速度势,进而得到了相应的内部动水力,最后采用梁单元有限元方法求解耦联运动方程。与解析方法和纯数值方法相比,这一方法计算相对简单、有效。算例表明,该方法计算具有较高精度;并能为实际的工程计算节省大量的时间。
A semi-analytical and semi-numerical approach for earthquake induced interior hydrodynamic force on rectangular hollow bridge pier is developed.Based on linear radiation wave theory,eigenfunction expansion method is used to format the potential of rigid movement and that of elastic vibration.Then interior hydrodynamic forces are obtained.The coupling kinetic equations is solved by FEM with beam elements.This method is a relatively simple and efficient approach.An example is presented to illustrate the accuracy of this method,simultaneously the example shows this method need much less time than solid FEM.
A semi-analytical and semi-numerical approach for earthquake induced interior hydrodynamic force on rectangular hollow bridge pier is developed.Based on linear radiation wave theory,eigenfunction expansion method is used to format the potential of rigid movement and that of elastic vibration.Then interior hydrodynamic forces are obtained.The coupling kinetic equations is solved by FEM with beam elements.This method is a relatively simple and efficient approach.An example is presented to illustrate the accuracy of this method,simultaneously the example shows this method need much less time than solid FEM.
引文
[1]Liaw C Y,Chopra A K.Dynamics of towers surrounded bywater[J].Earthquake Engineering and Structural Dynam-ics,1974,3:33-49.
[2]Goto H,Toki K.Vibration characteristics and aseismic de-sign of submerged bridge piers[C]//Proceedings of theThird World Conference on Earthquake Engineering:Vol 2.Auckland and Wellington:NewZealand National Committeeon Earthquake Engineering,1965:107-125.
[3]Yoshihiro T,Robert TH.Restoring forces on vertical circu-lar cylinders forced by earthquakes[J].Earthquake Engi-neering and Structural Dynamics,1988,16:99-119.
[4]居荣初,曾心传.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983.
[5]Anthony N W.Earthquake response of submerged circularcylinder[J].Ocean Engineering,1986,13(6):569-585.
[6]Bhatta D D,Rahman M.Wave loadings on a vertical cylin-der due to heave motion[J].International Journal of Mathe-matics and Mathematical Sciences,1995,18(1):151-170.
[7]Bhatta D D,Rahman M.On scattering and radiation problemfor a cylinder in water of finite depth[J].International Jour-nal of Engineering Science,2003,41(2):931-967
[8]Lai Wei,Wang Junjie,Hu Shide.Earthquake induced hy-drodynamic pressure on bridge pier[J].Journal of TongjiUniversity,2004,32(1):1-5.[赖伟,王君杰,胡世德.地震下桥墩动水压力分析[J].同济大学学报,2004,32(1):1-5.]
[9]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,2004.
[10]Nilrat F B.Hydrodynamic pressure and added mass for ax-isymmetric bodies[R].Earthquake Engineering ResearchCenter,1980.
[11]王勖成.有限单元法[M].北京:清华大学出版社,2003.
[2]Goto H,Toki K.Vibration characteristics and aseismic de-sign of submerged bridge piers[C]//Proceedings of theThird World Conference on Earthquake Engineering:Vol 2.Auckland and Wellington:NewZealand National Committeeon Earthquake Engineering,1965:107-125.
[3]Yoshihiro T,Robert TH.Restoring forces on vertical circu-lar cylinders forced by earthquakes[J].Earthquake Engi-neering and Structural Dynamics,1988,16:99-119.
[4]居荣初,曾心传.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983.
[5]Anthony N W.Earthquake response of submerged circularcylinder[J].Ocean Engineering,1986,13(6):569-585.
[6]Bhatta D D,Rahman M.Wave loadings on a vertical cylin-der due to heave motion[J].International Journal of Mathe-matics and Mathematical Sciences,1995,18(1):151-170.
[7]Bhatta D D,Rahman M.On scattering and radiation problemfor a cylinder in water of finite depth[J].International Jour-nal of Engineering Science,2003,41(2):931-967
[8]Lai Wei,Wang Junjie,Hu Shide.Earthquake induced hy-drodynamic pressure on bridge pier[J].Journal of TongjiUniversity,2004,32(1):1-5.[赖伟,王君杰,胡世德.地震下桥墩动水压力分析[J].同济大学学报,2004,32(1):1-5.]
[9]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,2004.
[10]Nilrat F B.Hydrodynamic pressure and added mass for ax-isymmetric bodies[R].Earthquake Engineering ResearchCenter,1980.
[11]王勖成.有限单元法[M].北京:清华大学出版社,2003.
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