Design and validation of test model for structural vibration of overpass with track box girder
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摘要: 基于π定理和量纲分析法，推导了某32 m高架轨道箱梁结构缩尺模型与原型物理量之间的相似关系，并通过建立动力仿真模型进行计算，验证了相似关系的准确性；以该相似关系指导设计，并通过合理选材，制作了几何相似比为10∶1的轨道箱梁结构缩尺试验模型；通过激振试验获取了缩尺试验模型的模态频率、振型和加速度响应，并与有限元仿真结果对比，验证了缩尺试验模型的有效性；在此基础上利用该缩尺试验模型研究了轨道箱梁结构的振动传递特性。研究结果表明：高架轨道箱梁缩尺模型与原型结构前10阶模态频率误差均小于1%，且由缩尺模型计算结果反演的加速度响应曲线与原型结果趋势一致，模型与原型之间相似关系推导正确；缩尺试验模型实测模态频率与有限元仿真结果的误差均在8.8%以内，各阶模态振型吻合，且实测加速度响应随时间变化趋势与有限元仿真结果一致，制作的高架轨道箱梁结构缩尺试验模型有效；当振动在轨道结构中传递时，扣件和橡胶层对1 000 Hz以上的高频振动具有明显的衰减作用；当振动由箱梁顶板向底板传递时，顶板加速度导纳最大，翼板次之，其次是腹板，底板加速度导纳最小；设计制作的高架轨道箱梁结构缩尺试验模型能够反映原型振动响应的一般传递规律，可用于轨道箱梁结构振动传递特性与控制关键技术研究。Abstract: Based on the π theory and the dimensional analysis method, the similarity relationship of physical quantities between the scale model and the prototype of a 32 m overpass with track box girder structure were deduced. The accuracy of similarity relationship was verified via the dynamic simulation. By considering the similarity relationship as design guides and selecting materials rationally, a scale test model of track box girder structure with a geometric similarity ratio of 10∶1 was constructed. The modal frequencies, vibration modes, and acceleration responses of the scale test model were obtained via the excitation test, and the results were compared with the finite element simulation results to validate the scale test model. Using the model, the vibration transmission characteristics of track box girder structure were studied. Research results demonstrate that the deviations of the first 10 order modal frequencies between the scale model of overpass with track box girder and the prototype structure are less than 1%. The acceleration response curve obtained for the scale model is consistent with that obtained for the prototype. The deduced similarity relationship between the scale model and the prototype is accurate. The errors between the measured modal frequencies of the scale test model and the finite element simulation results are less than 8.8%. In addition, the vibration modes are consistent for all orders, and the measured acceleration response variations with respect to time are consistent with the finite element simulation results. Hence, the constructed scale test model of overpass with track box girder structure is reliable. When the vibration transmits in the track structure, the fasteners and rubber layer have evident attenuation effects for high-frequency vibrations (at frequencies above 1 000 Hz). When the vibration transmits from the top plate to the bottom plate of box girder, the top plate acceleration admittance is the largest, followed by that of the wing plate and then that of the web. The bottom plate acceleration admittance is the smallest. The scale test model of overpass with track box girder structure can reflect the general transmission law of vibration responses of prototype. Therefore, the model can be used to study the vibration transmission characteristics and control technology of track box girder structures. 6 tabs, 20 figs, 31 refs.
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Key words:
- bridge engineering /
- similar model /
- track box girder structure /
- excitation test /
- modal /
- acceleration
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图 1 缩尺模型与原型结构顶板加速度对比
Figure 1. Acceleration comparison of top plate between scale model and prototype structure
图 18 试验与仿真顶板加速度对比
Figure 18. Comparison of top plate acceleration between test and simulation
表 1 模型试验相似关系
Table 1. Similarity relationships of model test
物理参数 相似关系 备注 箱梁弹性模量E1 CE1 基本量 几何尺寸L CL 基本量 箱梁密度ρ1 Cρ1 基本量 泊松比μ Cμ=1 导出量 底座板弹性模量E2、轨道板弹性模量E3、钢轨弹性模量E4 CE2=CE3=CE4=CE1 导出量 响应位移δ Cδ=CL 导出量 底座板密度ρ2、轨道板密度ρ3、钢轨密度ρ4 Cρ2=Cρ3=Cρ4=Cρ1 导出量 截面惯性矩I CI=C4L 导出量 荷载F CF=CE1C2L 导出量 质量m Cm=Cρ1C3L 导出量 刚度k Ck=CE1CL 导出量 阻尼c Cc=C2LC1/2E1C1/2ρ1 导出量 时间T CT=(Cρ1/CE1)1/2CL 导出量 频率f Cf=CL－1(CE1/Cρ1)1/2 导出量 响应速度v Cv=(CE1/Cρ1)1/2 导出量 响应加速度a Ca=CE1/(Cρ1CL) 导出量 重力加速度g 忽略 导出量 
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表 2 原型与模型材料参数
Table 2. Material parameters of prototype and model
构件 物理量 原型 模型 钢轨 密度/(kg·m-3) 7 800 9 750 弹性模量/GPa 210 140 泊松比 0.3 0.3 轨道板 密度/(kg·m-3) 2 500 3 125 弹性模量/GPa 36.2 24.1 泊松比 0.2 0.2 底座板 密度/(kg·m-3) 2 400 3 000 弹性模量/GPa 34 22.7 泊松比 0.15 0.15 箱梁 密度/(kg·m-3) 2 500 3 125 弹性模量/GPa 36.2 24.1 泊松比 0.2 0.2 扣件 竖向刚度/(MN·m-1) 60 4 竖向阻尼/(kN·s·m-1) 10 0.09 CA砂浆 竖向刚度/(MN·m-1) 1200 80 竖向阻尼/(kN·s·m-1) 83 0.76 支座 竖向刚度/(MN·m-1) 3 380 225.3 竖向阻尼/(kN·s·m-1) 100 0.91
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表 3 模态频率对比
Table 3. Modal frequency comparison
阶次 1 2 3 4 5 6 7 8 9 10 缩尺模型/Hz 38.206 44.707 69.435 81.237 87.356 87.356 87.356 87.356 96.513 111.130 缩尺反演/Hz 5.230 6.120 9.506 11.121 11.959 11.959 11.959 11.959 13.213 15.214 原型/Hz 5.231 6.122 9.507 11.124 12.019 12.019 12.019 12.019 13.215 15.217 误差/% 0.019 0.033 0.011 0.027 0.500 0.500 0.500 0.500 0.015 0.020
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表 4 模型试验相似常数
Table 4. Similarity constants of model test
序号 物理参数 相似常数 1 E1 1.206 7 2 L 10 3 ρ1 1.134 5 4 μ 1 5 E2、E3、E4 1.206 7 6 δ 10 7 ρ2、ρ3、ρ4 1.134 5 8 I 10 000 9 F 120.67 10 m 1 134.5 11 k 12.067 12 c 117.004 3 13 T 9.696 1 14 f 0.103 0 15 v 1.031 3 16 a 0.106 4
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表 5 模型主要结构参数相似结果
Table 5. Similarity results of main structural parameters of model
试验值 E2/GPa E3/GPa E4/GPa ρ2/(kg·m-3) ρ3/(kg·m-3) ρ4/(kg·m-3) 原型值 34 36 210 2 400 2 500 7 800 目标值 28.20 29.80 174.03 2 115.50 2 203.60 6 875.30 模型值 32.7 28.8 174.0 2 149.0 2 253.0 6 870.0 偏差/% 16.00 3.40 0.02 1.60 2.20 0.08
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表 6 箱梁自由模态频率
Table 6. Free-modal frequencies of box girder
阶次 仿真模态频率/Hz 实测模态频率/Hz 相对误差/% 1 124.441 125.662 0.98 2 164.845 150.340 8.80 3 232.183 231.151 0.44 4 233.226 5 253.072 249.441 1.43
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