移动荷载作用下黏弹性地基-Timoshenko梁振动响应对比分析  

Comparative Analysis of Dynamic Responses of Timoshenko Beams on Visco-Elastic Foundations Under Moving Loads

作　　者：黄强 刘干斌 律清 黄宏伟[3] 郑荣跃 HUANG Qiang;LIU Ganbin;Lü Qing;HUANG Hongwei;ZHENG Rongyue(Institute of Geotechnical Engineering,Ningbo University,Ningbo,Zhejiang 315211,P.R.China;School of Civil and Transportation Engineering,Ningbo University of Technology,Ningbo,Zhejiang 315211,P.R.China;Department of Geotechnical Engineering,Tongji University,Shanghai 200092,P.R.China)

机构地区：[1]宁波大学岩土工程研究所,浙江宁波315211 [2]宁波工程学院建筑与交通工程学院,浙江宁波315211 [3]同济大学地下建筑与工程系,上海200092

出　　处：《应用数学和力学》2020年第7期748-759,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(面上项目)(51778303);国家自然科学基金(重点项目)(51538009);宁波市自然科学基金(2019A610399)。

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.The dynamic responses of 3 D, 2 D and 1 D 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 3 D track-ground model, which is a function of the wave number and the frequency. The critical velocities of 2 D and 3 D track-ground models are almost the same, but are much smaller than that of the 1 D model. When the load speed is less than the critical speed, the Timoshenko beam deflection of the 3 D model is the smallest, that of the 2 D model is the intermediate, and that of the 1 D model is the largest. However, when the load speed reaches or exceeds the critical velocity, the T beam deflection of the 2 D model becomes the largest, and the time history curves of the T beam deflection for the 3 models are significantly different. In the 2 D and 3 D 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.

关 键 词：移动荷载 TIMOSHENKO梁 地基等效刚度 临界速度 地基位移 

分 类 号：U213.2[交通运输工程—道路与铁道工程]