地基上下震动时高桥墩的动力屈曲
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摘要
考虑大变形的影响,建立高桥墩在地震波冲击下引起的地基上下震动时的非线性动力学基本方程式;通过位移形函数假设,采用伽辽金积分方法得到了时间变率的动力学控制方程;对时间变率的非线性微分方程进行数值求解,给出了同一地震波不同强度下高桥墩的位移响应曲线以及从产生横向振动到失稳的全过程;得到了地震波冲击时高桥墩失稳的临界地震加速度和失稳时刻。通过数值算例比较了地震波幅值、高桥墩柔度以及桥面质量大小对位移幅值响应曲线、临界地震加速度和失稳时刻的影响。
Considering the influence of large deformation,the non-linear dynamic equations of high pier under perpendicular foundation motion induced by earthquake were established.By supposing the displacement shape function and applying the Galerkin method,the dynamic equations with respect to time were derived.By numerical calculation,the displacement response curves of the high pier under perpendicular foundation motion induced by earthquake with different magnitudes were obtained and the overall process from the beginning of transverse vibration to the entering into unstable state of the high pier were presented.The critical seismic acceleration and the moment of instability occurence were acquired.The influence of seismic peak,slenderness ratio and weight of the bridge on displacement response,critical seismic acceleration and instability occurence moment were analyzed.
Considering the influence of large deformation,the non-linear dynamic equations of high pier under perpendicular foundation motion induced by earthquake were established.By supposing the displacement shape function and applying the Galerkin method,the dynamic equations with respect to time were derived.By numerical calculation,the displacement response curves of the high pier under perpendicular foundation motion induced by earthquake with different magnitudes were obtained and the overall process from the beginning of transverse vibration to the entering into unstable state of the high pier were presented.The critical seismic acceleration and the moment of instability occurence were acquired.The influence of seismic peak,slenderness ratio and weight of the bridge on displacement response,critical seismic acceleration and instability occurence moment were analyzed.
引文
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[2]汪优,赵明华,黄靓.桥梁基桩屈曲机理及其分析方法[J].中南公路工程,2005,30(4):22-26.
[3]严东晋,宋启根.结构冲击屈曲准则讨论[J].工程力学,1997,11(4):18-28.
[4]Bakker M C M.Shear-flexural buckling of cantilever columnsunder uniformly distributed load[J].Journal of EngineeringMichanics,2006,132(11):1160-1167.
[5]Luo S N,Fu Y M,Cao Z Y.Non-linear vibration of compositebeams with an arbitrary delamination[J].Journal of Soundand Vibration,2004,271:535-545.
[6]孙强.伸出地面上基桩的动力稳定性研究[J].岩土工程学报,2003,25(4):459-462.
[7]孙强.竖向动荷载下桩土参数对基桩动力稳定性的影响[J].工程抗震,2004,3(3):33-37.
[8]孙强.竖向谐振荷载下摩擦桩的横向振动性能研究[J].振动与冲击,2006,25(4):85-87.
[9]罗松南,李礼,周慧,等.冲击荷载下两端简支高桥墩的动力屈曲[J].振动与冲击,2009,28(12):1-3.
[10]罗松南,傅衣铭,曹志远。梁非线性动力分析中剪切力和轴力的相互影响[J].湖南大学学报,1999,6(3):9-12.
[11]王德禹.受静载作用的直杆在轴向冲击荷载下的屈曲[J].振动与冲击,1997,16(1):35-37.
[12]郭修武.公路桥梁构件自重标准值的确定[J].中国公路学报,1997,10(1):33-38.
[13]丁秋琴,高艳玲,苗春兰.全球7级以上大地震及中国4级以上地震目录[J].地震,2009,29(4):147-170.
[14]郝文化.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2005.
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