Lower Vertical Frequency Limit for Simply Supported Box-Girder on Moscow-Kazan High-Speed Railway Line
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摘要: 为研究莫-喀高速铁路简支箱梁竖向下限基频，通过理论公式计算预应力混凝土简支箱梁的竖向基频，建立有限元模型，根据设计荷载效应大于等于实际运营车辆荷载效应的原则，确定梁体容许动力系数；基于移动荷载模型进行动力仿真分析，得到列车作用下简支箱梁的实际动力系数；提出了设计速度250、300、350 km/h和400 km/h简支箱梁竖向自振基频的下限值. 研究表明：梁体动力响应幅值均在其一阶竖弯频率出现波峰；通过调节桥梁的竖向自振基频，避开列车对桥梁的竖向激振频率可以有效降低振动波峰；建议设计速度250、300、350 km/h和400 km/h跨度33.1 m预应力混凝土简支箱梁竖向自振基频分别为3.02、3.63、4.08 Hz和4.68 Hz.Abstract: To study the lower vertical basic frequency limit of a simply supported box-girder on the Moscow-Kazan high-speed railway line, firstly, the vertical fundamental frequency of the prestressed concrete (PC) simply supported box-girder was calculated with theoretical formula. Then, according to the principle of the bridge dynamic effect under the action of a moving train should not surpass that of the designed value, the allowable impact factor of the girder was determined by utilizing the finite element method. Secondly, based on the moving load model, the dynamic simulation analysis was conducted to obtain the impact factor of the simply supported box-girder under a moving train. Finally, the lower vertical basic frequency limits of the PC simply supported box-girder for design speeds of 250, 300, 350 km/h, and 400 km/h were recommended. The results show that the peak of the dynamic response amplitude of the girder will appear at the first bend natural frequency. Adjusting the vertical basic frequency of the bridge can effectively reduce the vibration peak, which compensates for the vertical excitation frequency caused by the moving train. The lower vertical basic frequency limits of the 33.1 m span PC simply supported box-girder for design speeds of 250, 300, 350 km/h, and 400 km/h are recommended as 3.02, 3.63, 4.08 Hz, and 4.68 Hz, respectively.
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表 1 车辆参数
Table 1. Vehicle parameters
参数 CRH3 ICE2 ЭBC1 × 2 Lv/m 24.825 26.400 24.730 Lc/m 17.375 19.000 17.370 Lw/m 2.5 2.5 2.6 最大轴荷载/kN 166.6 195.0 165.0 一般轴荷载/（kN•m–1） 27.18 19.23 25.07 
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表 2 基频系数统计表
Table 2. Basic frequency factors statistics
速度/（km•h–1） CRH3 ICE2 ЭBC1 × 2 包络值 250 90 100 100 100 300 110 120 120 120 350 130 135 135 135 400 145 155 155 155
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