移动简谐荷载作用下层状地基-轨道耦合系统动力响应分析

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (12) : 61-70.

论文

巴振宁1，2，金威1，梁建文1,2

作者信息 +

Dynamic responses of layered foundation-track coupled system due to moving harmonic loads

Ba zhenning1,2, Jin wei1, Liang Jianwen1,2

Author information +

文章历史 +

摘要

采用格林函数方法求解层状地基-轨道耦合系统在移动简谐荷载作用下的动力响应问题。通过求解层状地基表面作用移动均布线荷载时的动力格林影响函数，由位移连续条件实现层状地基与轨道的耦合，求得移动简谐荷载作用下频率-波数域内的系统动力响应，最后通过傅里叶逆变换求得时间-空间域内的动力响应。与已有结果的比较验证了方法的正确性，并以均匀半空间地基和基岩上单一土层地基-欧拉梁耦合系统为模型，研究荷载振动频率、移动速度、地基刚度以及土层厚度对动力响应的影响。研究表明移动简谐荷载频率较高时与移动静荷载情况不同，不再具有跨音速时地表位移幅值最大的规律；成层地基-轨道耦合系统在移动简谐荷载作用下的动力响应与均匀地基情况存在显著差异，当荷载频率与层状地基固有频率接近时，地基表面位移幅值较大；另外随着基岩与土层剪切波速比的增大，荷载以超音速经过后地基表面位移振动更加剧烈，振动时间更长，随着土层厚度的增大，位移幅值逐渐向低频区域迁移。

Abstract

The dynamic responses of layered foundation-track coupled system due to moving harmonic loads are evaluated by using the Green’s Functions method. The results are firstly obtained in the frequency-wave number domain and then results in the time-space domain are obtained by using the inverse Fourier transformation, and to do this, the Green’s Functions of moving distributed vertical loads acting on the surface of a layered half-space are deduced based on the three-dimensional exact dynamic stiffness matrix. The validity of the method are confirmed by comparing results with published ones, and the effects of the frequencies and velocities of the moving load, and in particular, some effects of layering on the dynamic responses are studied by taking layered ground-track coupled system and uniform ground-track coupled system as examples. The results show that the maximum ground surface displacements for the moving harmonic loads may not occur at the transonic speed compared to the moving static loads cases. The dynamic responses of layered foundation-track coupled system are significantly different from those of the uniform case. The amplitudes of the surface ground displacement are much larger when the frequency of the load is close to the natural frequency of the layered ground. The displacement amplitudes of the ground vibrate more serious with much longer duration when the load past by with a supersonic speed as the shear wave velocity ratio between the bedrock and the soil layer become larger. And the frequency spectrums of the displacement amplitudes migrate to the low frequency regions as the depth of the layer becomes thicker.

导出引用

巴振宁1，2，金威1，梁建文1,2. 移动简谐荷载作用下层状地基-轨道耦合系统动力响应分析[J]. 振动与冲击, 2016, 35(12): 61-70

Ba zhenning1,2, Jin wei1, Liang Jianwen1,2. Dynamic responses of layered foundation-track coupled system due to moving harmonic loads[J]. Journal of Vibration and Shock, 2016, 35(12): 61-70

参考文献

[1] Sneddon IN., The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid, Rend CirMater
[2] Eason G., The stresses produced in a semi-infinite solid by a moving surface force, Int J Eng Sci, 1965, 2: 581~609
[3] Gakenheimer DC., Miklowtz J., Transient excitation of all elastic half space by a point load traveling on the surface. Journal of Applied Mechanics, 1969, 36: 505~515
[4] De Barros FCP., Luco JE., Response of a layered viscoelastic half space to a moving point load, Wave Motion, 1994, 19: 189~210
[5] Grundmann H., Lieb M., Trommer E., The response of a layered half-space to traffic loads moving along its surface, Archive of Applied Mechanics, 1999, 69(1): 55~67
[6] 徐斌, 陆建飞, 王建华, 等. 移动荷载作用下层状饱和土的动力响应[J]. 岩土力学, 2008, 29(12): 3186-3192(Xu Bin, Lu Jianfei, Wang Jianhua, et al. Dynamic response of layered saturated soil under moving loads[J]. Rock and Soil Mechanics, 2008, 29 (12): 3186-3192(in Chinese))
[7] Lu JF., Jeng DS., A half-space saturated poro-elastic medium subjected to a moving point load, International Journal of Solids and Structure, 2007, 44: 573-586
[8] 刘干斌，汪鹏程，陈运平，姚海林，矩形运动荷载作用下软土地基的三维振动研究，岩土力学，2006，27（10）：1658-1662(Liu Ganbin, Wang Pencheng, Yao Hailin, Chen Yunping. 3D ground vibration of a soft subgrade in the vicinity of a moving rectangular load[J]. Rock and Soil Mechanics, 2006, 27 (10): 1658-1662(in Chinese))
[9] 陈远国, 金波. 移动简谐荷载作用下多孔地基的动力响应[J]. 中国科学: G 辑, 2008, 38(3): 250-259(Chen Yuanguo, Jin Bo, Dynamic response of layered saturated soil under moving loads[J]. Science in China:Series G, 2008,38(3): 250-259(in Chinese))
[10] Kaynia MA., Madshus C., Zackrisson P., Ground vibration from high-speed trains, prediction and countermeasure, Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(6): 531-537
[11] Takemiya H., Bian XC., Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage, J Eng Mech, 2005, 131: 699~711
[12] 边学成, 陈云敏. 列车移动荷载作用下分层地基响应特性[J]. 岩石力学与工程学报, 2007, 26(1): 182-189(Bian Xuecheng, Chen Yunmin. Characteristics of layered ground responses under train moving loads[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(1): 182-189(in Chinese))
[13] 边学成, 陈云敏, 胡婷. 基于 2.5 维有限元方法模拟高速列车产生的地基振动[J]. 中国科学: G 辑, 2008, 38(5): 600-617(Bian Xuecheng,Chen Yunmin,Hu ting.Numerical simulation of high-speed train induced ground vibrations using 2.5 D finite element approach[J]. Science in China: Series G, 2008, 38(5): 600-617(in Chinese))
[14] 蔡袁强, 孙宏磊, 徐长节. 轨道刚度对路轨系统及饱和地基动力响应的影响[J]. 岩土工程学报, 2007, 29(12): 1787-1793(Cai Yuanqiang, Sun Honglei, Xu Changjie. Effect of rail rigidity on track-ground vibrations due to a high-speed train[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(12): 1787-1793(in Chinese))
[15] 孙宏磊, 蔡袁强, 徐长节. 移动列车荷载作用下路轨系统及饱和半空间土体动力响应[J]. 岩石力学与工程学报, 2007, 26(8): 1705-1712(Sun Honglei, Cai Yuanqiang, Xu Changjie. Dynamic response of track system and saturated soil in half space subjected to a moving train load[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(8): 1705-1712(in Chinese))
[16] 高广运, 李宁, 何俊锋, 高盟. 列车移动荷载作用下饱和地基的地面振动特性分析[J]. 振动与冲击, 2011, 30(6): 86-92(Gao Guangyun, Li Ning, He Junfeng, Gao Meng. Analysis of ground vibration generated by train moving loads on saturated soil[J]. Journal of Vibration and Shock, 2011, 30(6): 86-92(in Chinese))
[17] 高广运, 何俊锋, 杨成斌, 赵元一. 2.5 维有限元分析饱和地基列车运行引起的地面振动[J]. 岩土工程学报, 2011, 33(2): 234-241(Gao Guangyun, He Junfeng, Yang Chengbin, Zhao Yuanyi. Ground vibration induced by trains moving on saturated ground using 2.5 D FEM[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(2): 234-241(in Chinese))
[18] Sheng X., Jones CJC., Petyt M., Ground vibration generated by a harmonic load acting on a railway track, Journal of Sound and Vibration, 1999, 225(1): 3-28
[19] Sheng X., Jones CJC., Thompson DJ., A theoretical study on the influence of the track on train-induced ground vibration, Journal of Sound and Vibration, 2004, 272(3): 909-936
[20] Auersch L., The excitation of ground vibration by rail traffic: theory of vehicle–track–soil interaction and measurements on high-speed lines, Journal of Sound and Vibration, 2005, 284(1): 103-132
[21] Steenbergen MJMM., Metrikine AV., The effect of the interface conditions on the dynamic response of a beam on a half-space to a moving load, European Journal of Mechanics-A/Solids, 2007, 26(1): 33-54
[22] 蔡袁强，王玉，曹志刚，徐长节，列车运行时由轨道不平顺引起的地基振动研究，岩土力学，2012，32（2）：327-335(Cai Yuanqiang, Wang Yu, Cao Zhigang, Xu Changjie. Study of ground vibration from trains caused by track irregularities[J]. Rock and Soil Mechanics, 2012, 32 (2): 327-335(in Chinese))
[23] 梁建文, 巴振宁. 弹性层状半空间中沉积谷地对入射平面 SH 波的放大作用[J]. 地震工程与工程振动, 2007, 27(3): 1-9(Liang Jianwen, Ba Zhenning. Surface motion of an alluvial valley in layered half-space for incident plane SH waves [J]. Journal of Earthquake Engineering and Engineering Vibration, 2007, 27(3): 1-9(in Chinese))
[24] 梁建文, 巴振宁. 三维层状场地的精确动力刚度矩阵及格林函数[J]. 地震工程与工程振动, 2007, 27(5): 7-17(Liang Jianwen, Ba Zhenning. Exact dynamic stiffness matrices of 3-D layered sites and its Green’s function[J]. Journal of Earthquake Engineering and Engineering Vibration, 2007, 27(5): 7-17(in Chinese))
[25] 巴振宁，梁建文，金威，高速移动列车荷载作用下成层地基-轨道耦合系统的动力响应[J]. 土木工程学报, 2014, 47(11):108-119(Ba Zhenning, Liang Jianwen, Jin Wei. Dynamic responses of layered ground-track coupled system due to high-speed train moving loads[J].China Civil Engineering Journal,2014, 47(11): 108-119(in Chinese))
[26] 巴振宁, 金威, 梁建文. 层状饱和地基-轨道-列车耦合系统轨道不平顺引起的振动分析[J]. 振动与冲击, 2015, 34(15): 88-97(Ba Zhenning, Jin Wei, Liang Jianwen. Vibration analysis of layered saturated ground-track-vehicle coupling system induced by track irregularities[J]. Journal of Vibration and Shock, 2015, 34(15): 88-97(in Chinese)