地基水平运动时高桥墩的动力屈曲
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摘要
考虑大变形的影响,建立了高桥墩在地震波冲击下引起的地基水平运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acr和失稳时刻。通过数值算例比较了地震波幅值、高桥墩柔度、桥面质量大小对位移幅值响应、临界地震加速度、失稳时刻等参数的影响。算例表明当发生7.5级以上地震时,桥墩会有较大程度的破坏。
Considering the influence of the large deformation,the non-linear dynamic equations of high pier under the foundation horizontal motion by earthquake are established.By supposing the displacement shape function and applying the Galerkin method,the dynamic equations about time are obtained.By numerical calculation,the displacement response curves of the high pier under the foundation horizontal motion by earthquake with different magnitude and the overall process from the transverse vibration to the instability of the high pier are given.The critical seismic acceleration acr and the instability time are obtained.The influence of the different seismic peak,the slenderness ratio and the weight of the bridge on the displacement response,the critical seismic acceleration and the instability time are analyzed.The example shows that when an Ms7.5 or above earthquake happens,piers will have a greater degree of damage.
Considering the influence of the large deformation,the non-linear dynamic equations of high pier under the foundation horizontal motion by earthquake are established.By supposing the displacement shape function and applying the Galerkin method,the dynamic equations about time are obtained.By numerical calculation,the displacement response curves of the high pier under the foundation horizontal motion by earthquake with different magnitude and the overall process from the transverse vibration to the instability of the high pier are given.The critical seismic acceleration acr and the instability time are obtained.The influence of the different seismic peak,the slenderness ratio and the weight of the bridge on the displacement response,the critical seismic acceleration and the instability time are analyzed.The example shows that when an Ms7.5 or above earthquake happens,piers will have a greater degree of damage.
引文
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[15]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.
[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 columns underuniformly distributed load[J].Journal of Engineering Michanics,2006,132(11):1160-1167.
[5]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.
[6]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.
[7]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.
[8]崔艳,韩志军,路国运,等.刚性快轴向冲击圆柱壳动力屈曲的计算机模拟[J].科学技术与工程,2010,10(5):1105-1108.
[9]阿尔乔姆H S,艾登L,黄雅意.梁-柱体系在椭圆型荷载作用下的精确解和动力屈曲分析[J].应用数学和力学,2010,31(10):1249-1255.
[10]韩志军,程国强,马宏伟,等.弹塑性杆在刚性块轴向撞击下的动力屈曲[J].应用数学和力学,2006,27(3):337-341.
[11]韩强,黄怀纬,樊学军.弹性浅拱的非线性动力屈曲[J].华南理工大学学报:自然科学版,2010,38(3):1-7.
[12]罗松南,李礼,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.
[13]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.
[14]刘利斌,王伟.四阶Runge-Kutta算法的优化分析[J].成都大学学报,2007,3(1):19-21.
[15]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.
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