Vibration reduction of high-speed railway subgrade with periodic structures based on complex dispersion curves
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摘要: 目前对周期排桩衰减域的研究只停留在频散曲线分析阶段,只有少数学者利用二维复频散曲线来研究周期排桩衰减域,而频散曲线只能得到衰减域的范围,复频散曲线能得到振动波在衰减域内的衰减程度。利用COMSOL PDE模块求解三维模型的复频散曲线,通过对排桩排布形式和不同桩身材料的影响进行分析得到:三角形排布的排桩衰减域范围最广且减振效果最好;当桩身材料为混凝土或钢时,能产生高频衰减域,而使用两组元桩时可以产生低频衰减域,但两组元桩和混凝土桩的减振程度比钢桩小。最后,通过建立有限尺度的周期排桩频域响应模型验证了复频散曲线计算的正确性,同时对高铁荷载引起的地基振动特征频率0~50 Hz,提出针对不同频率减振的4种类型桩和1种组合桩,结果说明组合桩能结合4种类型排桩产生衰减域频率分布的特点,且减振效果较好。Abstract: At present, the researches on the attenuation zone of periodic row piles only stay in the stage of dispersion curve analysis. Only a few scholars have studied complex dispersion curves of 2D model. The dispersion curve can only obtain the range of the attenuation zone, while the complex dispersion curve can obtain its attenuation degree. In this study, the COMSOL PDE module is used to solve the complex dispersion curve of 3D model. By analyzing the influence of arrangement forms and materials of piles, it is found that the piles in triangular arrangement have the widest attenuation zone and the best vibration reduction effect. When the material of piles is concrete or steel, the attenuation zone in high frequency can be obtained, and the attenuation zone in low frequency can be obtained when two-component piles are used. The vibration reduction degrees of the two-component piles and concrete piles are smaller than those of the steel piles. Finally, a finite-scale frequency domain response model for periodic row piles is established to verify the correctness of the complex dispersion curve. As the characteristic frequency of the foundation vibration caused by the high-speed railway is within 0~50 Hz, four types of piles with different attenuation zones and one kind of composite piles are put forward. The results show that the composite piles can combine the attenuation zones of four types of row piles, and the vibration reduction effect is good.
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表 1 计算方案
Table 1 Calculation schemes
因素 水平 备注 示意图 排布形式 4 正方形排布(1号)、长方形排布(2号)、三角形排布(3号)、蜂窝形排布(4号) 桩身材料 3 混凝土(5号)、钢(6号)、橡胶+钢(7号) 注: 计算方案中一共设置了9种类型的排桩,第1,2,3,4号排桩对比讨论了排桩排布形式对衰减域的影响;第5,6,7号排桩对比讨论了桩身材料对衰减域的影响。表 2 材料参数
Table 2 Material properties
材料 弹性模量/MPa 泊松比 密度/(kg·m-3) 土 20 0.30 1800 钢 207000 0.30 7784 混凝土 30000 0.25 2500 橡胶 0.12 0.47 1300 完美匹配层 20 0.30 1800 表 3 计算方案
Table 3 Calculation schemes
方案 材料 半径/m 示意图 一 混凝土 0.8 二 钢 0.65 三 橡胶+钢 R=0.8r=0.75 四 橡胶+钢 R=0.95r=0.85 -
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