竖向地震作用下桥面与桥墩的多次重撞击力的计算
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摘要
采用简谐波形式的人工地震激励和瞬态波函数法,推导出了双跨连续梁桥在竖向地震激励下可能出现的多次弹性重撞击问题的理论解,采用组合体瞬态内力法,给出了多次重撞击力的求解方法。研究结果表明:该文方法可以合理模拟竖向地震作用下的桥面与桥墩间的多次重撞击现象,精确地求解复杂的多次重撞击力响应,模拟地震波和撞击瞬态波在结构内的传播过程,并可观察其中的"次撞击过程"。
Using the artificial earthquake ground motion in the form of a sinusoidal excitation, the theoretical solution of multiple elastic poundings between girder and pier of a single-pier and two-span bridge model under vertical earthquakes is derived from the expansion of transient wave functions in a series of eigenfunctions. The calculation method of multiple pounding forces is presented based on the transient internal force of the contact surface of the combined impact body. The numerical results show that the presented method can simulate reasonably the multiple-pounding phenomenon between girder and pier under vertical earthquakes. The multiple pounding force responses can be calculated in high precise. The propagations of earthquake wave and the pounding-induced transient waves throughout girder and pier can be depicted. The sub-pounding process can be observed from the numerical simulations as well.
Using the artificial earthquake ground motion in the form of a sinusoidal excitation, the theoretical solution of multiple elastic poundings between girder and pier of a single-pier and two-span bridge model under vertical earthquakes is derived from the expansion of transient wave functions in a series of eigenfunctions. The calculation method of multiple pounding forces is presented based on the transient internal force of the contact surface of the combined impact body. The numerical results show that the presented method can simulate reasonably the multiple-pounding phenomenon between girder and pier under vertical earthquakes. The multiple pounding force responses can be calculated in high precise. The propagations of earthquake wave and the pounding-induced transient waves throughout girder and pier can be depicted. The sub-pounding process can be observed from the numerical simulations as well.
引文
[1]Wang C J.Failure study of a bridge subjected to pounding and sliding under severe ground motions[J].International Journal of Impact Engineering,2007,34(2):216―231.
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[3]Ruangrassamee A,Kawashima K.Control of nonlinear bridge response with pounding effect by variable dampers[J].Engineering Structures,2003,25(5):593―606.
[4]Pantelides C P,Ma X.Linear and nonlinear pounding of structural systems[J].Computers&Structures,1998,66(1):79―92.
[5]Jankowski R,Wilde K,Fujino Y.Pounding of superstructure segments in isolated elevated bridge during earthquakes[J].Earthquake Engineering andStructural Dynamics,1998,27(5):487―502.
[6]李建中,范立础.非规则梁桥纵向地震反应及碰撞效应[J].土木工程学报,2005,38(1):84―90.Li Jianzhong,Fan Lichu.Longitudinal seismic response and pounding effects of girder bridges with unconventional configurations[J].China Civil Engineering Journal,2005,38(1):84―90.(in Chinese)
[7]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128―133.Li Zhongxian,Yue Fuqing,Zhou Li.Equivalent Kelvin impact model for pounding analysis of bridges during earthquake[J].Engineering Mechanics,2008,25(4):128―133.(in Chinese)
[8]Wang C,Kim J.New analysis method for a thin beam impacting against a stop based on the full continuous model[J].Journal of Sound and Vibration,1996,191(5):809―823.
[9]Yin X C,Qin Y,Zou H.Transient responses of repeated impact of a beam against a stop[J].International Journal of Solids and Structures,2007,44(22-23):7323―7339.
[10]Yin X C.Multiple impacts of two concentric hollow cylinders with zero clearance[J].International Journal of Solids and Structures,1997,34(35-36):4597―4616.
[11]Yin X C,Yue Z Q.Transient plane-strain response of multilayered elastic cylinders to axisymmetric impulse[J].ASME Journal of Applied Mechanics,2002,69(6):825―835.
[12]Hu B,Eberhard P.Simulation of longitudinal impact waves using time delayed systems[J].ASME Journal of Dynamic Systems Measurement and Control,2004,126(3):644―649.
[13]Paoli L.Time discretization of vibro-impact[J].Philosophical Transactions of the Royal Society of London Series A:Mathematical Physical and Engineering Sciences,2001,359(1789):2405―2428.
[14]周云,宗兰,张文芳.土木工程抗震设计[M].北京:科学出版社,2005.Zhou Yun,Zong Lan,Zhang Wenfang.Seismic design of civil engineering[M].Beijing:Science Press,2005.(in Chinese)
[15]钱培风,苏文藻,张悉德,杨亚弟.烟囱在地震作用下的纵波应力[J].力学学报,1978,10(2):125―134.Qian Peifeng,Su Wenzao,Zhang Xide,Yang Yadi.Longitudinal wave stress on chimneys during earthquakes[J].Chinese Journal of Theoretical and Applied Mechanics,1978,10(2):125―134.(in Chinese)
[2]Ruiz Julian F D,Hayashikawa T,Obata T.Seismic performance of isolated curved steel viaducts equipped with deck unseating prevention cable restrainers[J].Journal of Constructional Steel Research,2007,63(2):237―253.
[3]Ruangrassamee A,Kawashima K.Control of nonlinear bridge response with pounding effect by variable dampers[J].Engineering Structures,2003,25(5):593―606.
[4]Pantelides C P,Ma X.Linear and nonlinear pounding of structural systems[J].Computers&Structures,1998,66(1):79―92.
[5]Jankowski R,Wilde K,Fujino Y.Pounding of superstructure segments in isolated elevated bridge during earthquakes[J].Earthquake Engineering andStructural Dynamics,1998,27(5):487―502.
[6]李建中,范立础.非规则梁桥纵向地震反应及碰撞效应[J].土木工程学报,2005,38(1):84―90.Li Jianzhong,Fan Lichu.Longitudinal seismic response and pounding effects of girder bridges with unconventional configurations[J].China Civil Engineering Journal,2005,38(1):84―90.(in Chinese)
[7]李忠献,岳福青,周莉.地震时桥梁碰撞分析的等效Kelvin撞击模型[J].工程力学,2008,25(4):128―133.Li Zhongxian,Yue Fuqing,Zhou Li.Equivalent Kelvin impact model for pounding analysis of bridges during earthquake[J].Engineering Mechanics,2008,25(4):128―133.(in Chinese)
[8]Wang C,Kim J.New analysis method for a thin beam impacting against a stop based on the full continuous model[J].Journal of Sound and Vibration,1996,191(5):809―823.
[9]Yin X C,Qin Y,Zou H.Transient responses of repeated impact of a beam against a stop[J].International Journal of Solids and Structures,2007,44(22-23):7323―7339.
[10]Yin X C.Multiple impacts of two concentric hollow cylinders with zero clearance[J].International Journal of Solids and Structures,1997,34(35-36):4597―4616.
[11]Yin X C,Yue Z Q.Transient plane-strain response of multilayered elastic cylinders to axisymmetric impulse[J].ASME Journal of Applied Mechanics,2002,69(6):825―835.
[12]Hu B,Eberhard P.Simulation of longitudinal impact waves using time delayed systems[J].ASME Journal of Dynamic Systems Measurement and Control,2004,126(3):644―649.
[13]Paoli L.Time discretization of vibro-impact[J].Philosophical Transactions of the Royal Society of London Series A:Mathematical Physical and Engineering Sciences,2001,359(1789):2405―2428.
[14]周云,宗兰,张文芳.土木工程抗震设计[M].北京:科学出版社,2005.Zhou Yun,Zong Lan,Zhang Wenfang.Seismic design of civil engineering[M].Beijing:Science Press,2005.(in Chinese)
[15]钱培风,苏文藻,张悉德,杨亚弟.烟囱在地震作用下的纵波应力[J].力学学报,1978,10(2):125―134.Qian Peifeng,Su Wenzao,Zhang Xide,Yang Yadi.Longitudinal wave stress on chimneys during earthquakes[J].Chinese Journal of Theoretical and Applied Mechanics,1978,10(2):125―134.(in Chinese)
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