Comparative Analysis of Dynamic Responses of Timoshenko Beams on Visco-Elastic Foundations Under Moving Loads
-
摘要: 基于Fourier变换方法,对移动荷载作用下三维、二维和一维轨道地基模型的振动响应特征进行了研究,将轨道视为Timoshenko梁,比较了不同速度和地基厚度下各计算模型之间的响应差异.研究结果表明:三维模型存在一个地基等效刚度,为波数和频率的函数.二维和三维模型的临界速度较为接近,但比一维地基梁模型要小得多.荷载速度小于地基临界速度时,三维模型的梁挠度幅值最小,二维模型次之,一维模型梁挠度最大.当荷载速度达到或超过临界速度时,二维模型的梁挠度幅值变得最大,此时三者的挠度时程曲线存在明显差别.二维和三维模型的地层水平位移幅值先随地基深度增加而增大,在某一深度达到最大值后随深度增加逐渐减小,竖向位移幅值则随深度的增加逐渐减小.
-
关键词:
- 移动荷载 /
- Timoshenko梁 /
- 地基等效刚度 /
- 临界速度 /
- 地基位移
Abstract: The dynamic responses of 3D, 2D and 1D track-ground models under moving loads were analyzed based on the Fourier transformation technique. The track was modelled as a Timoshenko beam, and response discrepancies between the 3 models were compared in terms of different load speeds and ground thicknesses. The results indicate that, there is an equivalent ground stiffness in the 3D track-ground model, which is a function of the wave number and the frequency. The critical velocities of 2D and 3D track-ground models are almost the same, but are much smaller than that of the 1D model. When the load speed is less than the critical speed, the Timoshenko beam deflection of the 3D model is the smallest, that of the 2D model is the intermediate, and that of the 1D model is the largest. However, when the load speed reaches or exceeds the critical velocity, the T beam deflection of the 2D model becomes the largest, and the time history curves of the T beam deflection for the 3 models are significantly different. In the 2D and 3D models, the longitudinal ground displacement firstly increases with the soil depth to a peak value and then decreases, but the vertical displacement decreases continuously with the soil depth.-
Key words:
- moving load /
- Timoshenko beam /
- equivalent ground stiffness /
- critical velocity /
- ground displacement
-
[1] KRYLOV V V, DAWSON A R, HEELIS M E, et al. Rail movement and ground waves caused by high-speed trains approaching track-soil critical velocities[J]. Journal of Rail and Rapid Transit,2000,214(2): 107-116. [2] BIAN X C, CHENG C, JIANG J Q, et al. Numerical analysis of soil vibrations due to trains moving at critical speed[J]. Acta Geotechnica,2016,11(2): 281-294. [3] KENNEY J T. Steady state vibrations of beam on elastic foundation for moving load[J]. Journal of Applied Mechanics,1954,21(4): 359-364. [4] 杨燕, 丁虎, 陈立群. 车路耦合非线性振动高阶Galerkin截断研究[J]. 应用数学和力学, 2013,34(9): 881-890.(YANG Yan, DING Hu, CHEN Liqun. Nonlinear vibration of vehicle-pavement coupled system based on high-order Galerkin truncation[J]. Applied Mathematics and Mechanics,2013,34(9): 881-890.(in Chinese)) [5] 陈启勇, 胡少伟, 张子明. 基于声子晶体理论的弹性地基梁的振动特性研究[J]. 应用数学和力学, 2014,35(1): 29-38.(CHEN Qiyong, HU Shaowei, ZHANG Ziming. Research on the vibration property of the beam on elastic foundation based on the PCs theory[J]. Applied Mathematics and Mechanics,2014,35(1): 29-38.(in Chinese)) [6] METRIKINE A V, VROUWENVELDER A C M. Surface ground vibration due to a moving train in a tunnel: two-dimensional model[J]. Journal of Sound and Vibration,2000,234(1): 43-66. [7] ZHOU B, XIE X Y, YANG Y B. Simulation of wave propagation of floating slab track-tunnel-soil system by a 2D theoretical model[J]. International Journal of Structural Stability and Dynamics,2014,14(1): 1350051. [8] METRIKINE A V, KOPP K. Steady-state vibrations of an elastic beam on avisco-elastic layer under moving load[J]. Archive of Applied Mechanics,2000,70: 399-408. [9] 王常晶, 陈云敏. 移动荷载作用下弹性半空间Timoshenko梁的临界速度[J]. 振动工程学报, 2006,19(1): 139-144.(WANG Changjing, CHEN Yunmin. Critical velocities of Timoshenko beam on an elastic half-space under a moving load[J]. Journal of Vibration Engineering,2006,19(1): 139-144.(in Chinese)) [10] ANDERSEN L, JONES C J C. Coupled boundary and finite analysis of vibration from railway tunnels: a comparison of two-and three-dimensional models[J]. Journal of Sound and Vibration,2006,293(3/5): 611-625. [11] XU Q Y, XIAO Z C, LIU T, et al. Comparison of 2D and 3D prediction models for environmental vibration induced by underground railway with two types of tracks[J]. Computers and Geotechnics,2015,68: 169-183. [12] 陈镕, 万春风, 薛松涛, 等. Timoshenko梁运动方程的修正及其影响[J]. 同济大学学报(自然科学版), 2005,33(6): 711-715.(CHEN Rong, WAN Chunfeng, XUE Songtao, et al. Modification of motion equation of Timoshenko beam and its effect[J]. Journal of Tongji University(Natural Science),2005,33(6): 711-715.(in Chinese)) [13] JIN B. Dynamic displacements of an infinite beam on a poroelastic half space due to a moving oscillating load[J]. Archive of Applied Mechanics,2004,74(3): 277-287. [14] STEENBERG M, METRIKINE A V. The effect of the interface conditions on the dynamic response of a beam on a half-space to a moving load[J]. European Journal of Mechanics A: Solids,2007,26(1): 33-54. [15] HORVATH J S. New subgrade model applied to mat foundations[J]. Journal of Geotechnical Engineering,1983,109(12): 1567-1587. [16] 黄强, 黄宏伟, 张冬梅, 等. 移动简谐荷载作用下Kerr地基梁的稳态响应研究[J]. 振动与冲击, 2018,37(1): 14-21.(HUANG Qiang, HUANG Hongwei, ZHANG Dongmei, et al. Steady-state response of an infinite Euler-Bernoulli beam on Kerr foundation subjected to a moving oscillating load[J]. Journal of Shock and Vibration,2018,37(1): 14-21.(in Chinese))
点击查看大图
计量
- 文章访问数: 939
- HTML全文浏览量: 181
- PDF下载量: 278
- 被引次数: 0