Effects of rail pad viscoelasticity on vibration and structure-borne noise of railway box girder
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摘要: 以高速铁路WJ-7B型扣件胶垫为研究对象，通过动态力学性能试验测试了扣件胶垫在不同温度下的动力性能；结合温频等效原理、Williams-Landel-Ferry方程和高阶分数导数FVMP模型表征了扣件胶垫的黏弹性力学特性；将该模型代入建立的桥梁振动与结构噪声预测有限元-边界元模型，并与Kelvin-Vogit模型对比来分析扣件胶垫黏弹性对箱梁振动和结构噪声的影响。研究结果表明：扣件胶垫黏弹性表现为动参数的温频变特性，刚度与频率正相关，与温度负相关，阻尼与频率和温度均负相关，阻尼在1~100 Hz内变化明显，在100 Hz以上变化较小；扣件动参数测试值与高阶分数导数FVMP模型拟合值吻合良好，采用高阶分数导数FVMP模型可以准确描述扣件在宽温宽频下的动态黏弹性力学行为；仅考虑扣件胶垫频变特性时，桥梁在25~63 Hz振动加剧，在80~200 Hz振动减弱，在峰值频率63 Hz处顶板、腹板和底板的加速度振级分别增大5.62、0.91和2.94 dB，桥梁横桥向各板垂向近场点和梁底下方靠近地面处声辐射明显增大；同时考虑扣件胶垫温变与频变特性时，随着温度的降低，桥梁在31.5~50.0 Hz振动不断减小，在63~200 Hz振动不断增大，桥梁横桥向在顶板斜上方、腹板和底板垂向近场点和梁底下方靠近地面处声辐射减小，温度从20 ℃降到-20 ℃时，总体声压级最大降低了2 dB左右；忽略扣件胶垫黏弹性会导致桥梁振动和结构噪声预测产生偏差，仿真分析时应考虑扣件胶垫的黏弹性，以提高预测的准确性。Abstract: Taking the WJ-7B rail pad for high-speed railways as the research object, the dynamic properties of rail pad at different temperatures were tested through the dynamics mechanical property test, and the viscoelastic properties of rail pads were characterized by the temperature-frequency equivalent principle, Williams-Landel-Ferry (WLF) formula, and high-order fractional derivative fraction Voigt and Maxwell model in parallel (FVMP) model. The model was substituted into a finite element-boundary element model specially designed for the bridge vibration and structure-borne noise prediction, and the results were compared with those obtained through the Kelvin-Voigt (KV) model to analyze the effects of rail pad viscoelasticity on the box girder vibration and structure-borne noise. Research results show that the rail pad viscoelasticity is a temperature- and frequency-dependent dynamic parameter. The rail pad stiffness is positively correlated with the frequency and negatively correlated with the temperature, whereas the damping is negatively correlated with both the frequency and temperature. The damping changes significantly at frequencies within 1-100 Hz, but it varies slightly at frequencies above 100 Hz. The experimental dynamic parameters of rail pad are in good agreement with the high-order fractional derivative FVMP model fitting values. Therefore, the high-order fractional derivative FVMP model can accurately describe the dynamic viscoelastic behavior of rail pad under wide ranges of temperatures and frequencies. When only the frequency-dependent properties of rail pad are considered, the vibration of bridge intensifies at 25-63 Hz and weakens at 80-200 Hz. At the peak frequency of 63 Hz, the acceleration vibration levels of top plate, web, and bottom plate increase by 5.62, 0.91, and 2.94 dB, respectively. In the transverse direction of the bridge, the sound radiation increases obviously at the vertical near-field points of all bridge plates and near the ground under the bridge. When both the temperature- and frequency-dependent properties of rail pad are considered, as the temperature drops, the bridge vibration weakens continuously at 31.5-50.0 Hz and then intensifies progressively at 63-200 Hz. In the transverse direction of bridge, the sound radiation decreases diagonally above the top plate, at the vertical near-field points of web and bottom plate, and near the ground under the bridge. When the temperature drops from 20 ℃ to -20 ℃, the overall sound pressure level reduces by approximately 2 dB at most. Neglecting the rail pad viscoelasticity will lead to the deviations in the predictions of bridge vibration and structure-borne noise. The rail pad viscoelasticity should be considered in the simulation analysis to improve the prediction accuracy. 5 tabs, 15 figs, 31 refs.
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图 5 扣件胶垫在1~10 000 Hz和不同温度下的刚度和阻尼
Figure 5. Stiffnesses and dampings of rail pad under 1-10 000 Hz and different temperatures
图 10 桥梁跨中截面振动响应输出点
Figure 10. Vibration response output points in midspan section of bridge
表 1 高阶分数导数FVMP模型拟合参数
Table 1. Fitting parameters of high-order fractional derivative FVMP model
温度/℃ μ1 η1 μ2 η2 α β γ 20 12.9 6.63 1.53 20.1 0.48 0.55 0.14 0 13.6 2.92 4.96 30.2 0.46 0.56 0.22 -20 13.1 2.61 5.11 11.9 0.44 0.59 0.31 
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表 3 CRH380高速列车动力学参数
Table 3. Dynamics parameters of CRH380 high-speed train
动力学参数 数值 车体质量/kg 3.89×104 转向架质量/kg 3.06×103 轮对质量/kg 1.52×103 车体点头转动惯量/(kg·m2) 1.91×106 转向架点头转动惯量/(kg·m2) 3.20×103 一系悬挂刚度/(kN·m-1) 1772 一系悬挂阻尼/(kN·s·m-1) 20 二系悬挂刚度/(kN·m-1) 4500 二系悬挂阻尼/(kN·s·m-1) 20 车辆定距/m 17.5 固定轴距/m 2.5
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表 4 轨道和桥梁动力学参数
Table 4. Dynamics parameters of track and bridge
动力学参数 数值 钢轨弹性模量/Pa 2.060×1011 钢轨截面惯性矩/m4 3.217×10-5 钢轨单位长度质量/(kg·m-1) 60.64 扣件间距/m 0.64 轨道板质量/kg 7.956×103 轨道板弹性模量/Pa 3.450×1010 轨道板长度/m 6.4 轨道板宽度/m 2.55 轨道板高度/m 0.2 CA砂浆弹性模量/Pa 9.000×108 CA砂浆分布阻尼/(N·s·m-2) 2.220×105 一跨桥梁长度/m 32 桥梁弹性模量/Pa 3.450×1010 桥梁截面惯性矩/m4 6.196 4 桥梁单位长度质量/(kg·m-1) 1.182×104 桥梁阻尼比 0.05
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表 5 桥梁自振频率与振型
Table 5. Natural frequencies and modes of bridge vibration
阶数 频率/Hz 振型 1 4.02 横向侧倾 2 5.70 一阶竖弯 3 12.74 整体竖弯+侧倾 4 13.03 一阶反对称弯曲 5 13.85 整体扭转 6 18.25 二阶反对称弯曲 7 21.30 扭转+侧倾 8 25.19 顶板和翼缘局部振动 9 25.28 顶板和翼缘局部振动 10 26.10 顶板和翼缘局部振动
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