Stochastic Vibration Analysis of Maglev Train-Bridge Coupling System Based on Pseudo Excitation Method
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摘要:
为探讨随机轨道不平顺作用下中低速磁浮列车和桥梁的动力响应，将虚拟激励法引入磁浮车桥振动分析中，提出中低速磁浮车辆-悬浮控制系统-桥梁耦合系统随机振动分析方法. 将中低速磁浮列车简化为弹簧阻尼器连接的多刚体，悬浮系统中电流使用比例-微分（PD）控制方法进行主动控制，采用有限元方法对桥梁进行建模，将随机轨道不平顺转换为一系列简谐波构成的虚拟激励；编制中低速磁浮车桥动力系统随机振动分析程序，自动生成系统随机振动方程，利用分离迭代方法对磁浮车辆控制方程和桥梁动力方程进行求解计算. 研究结果表明：虚拟激励法能够高效计算中低速磁浮车桥系统随机动力响应，其计算效率约为蒙特卡洛方法的1/11，基于虚拟激励法能够获得中低速磁浮车桥动力系统均值、标准差和时变功率谱密度等统计结果.
Abstract:To explore the dynamic responses of medium-low speed maglev trains and bridges under stochastic track irregularities, the pseudo excitation method was introduced into the vibration analysis of the maglev train-bridge system. A stochastic vibration analysis method for the medium-low speed maglev train, suspension control system, and bridge coupling system was proposed. The medium-low speed maglev train was simplified as rigid bodies connected by spring dampers, and the current in the suspension system was actively controlled using the proportional-differential (PD) control method. The bridge was modeled by using a finite element method, and the stochastic track irregularity was converted into a pseudo excitation composed of a series of simple harmonic waves. The stochastic vibration analysis program for the medium-low speed maglev train-bridge dynamic system was developed, which could automatically generate the stochastic vibration equations of the system, and the separation iteration method was used to solve the control equation of the maglev train and the dynamic equation of the bridge. The research results indicate that the pseudo excitation method can efficiently calculate the stochastic dynamic response of the medium-low speed maglev train-bridge system, with a calculation efficiency of about 1/11 of the Monte Carlo method. Based on the pseudo excitation method, statistical results such as mean, standard deviation, and time-varying power spectral density of the medium-low speed maglev train-bridge dynamic system can be obtained.
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Key words:
- maglev train /
- train-bridge interaction /
- stochastic vibration /
- pseudo excitation method
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图 2 简支梁桥的截面图（单位：cm）
Figure 2. Cross-section of simply supported gride bridge （unit: cm）
图 3 磁浮车辆和桥梁竖向加速度均方根值
Figure 3. Root mean squares of vertical accelerations of maglev train and bridge
图 5 磁浮车桥系统动力响应的上、下限值
Figure 5. Upper and lower limits of dynamic responses of maglev train-bridge system
图 6 前车车体竖向、横向加速度时变功率谱密度
Figure 6. Time-varying power spectral density for vertical acceleration and lateral acceleration of leading train
图 7 第3跨桥梁跨中竖向、横向加速度时变功率谱密度函数
Figure 7. Time-varying power spectral density for midspan vertical acceleration and midspan lateral acceleration of three-span bridge
表 1 磁浮车辆主要参数
Table 1. Main parameters of maglev train
参数 取值 车体质量/kg 20 000 悬浮模块质量/kg 1 000 车体绕 x 轴转动惯量/（kg·m2） 66 800 车体绕 y 轴转动惯量/ （kg·m2） 210 000 车体绕 z 轴转动惯量/（kg·m2） 193 000 悬浮模块绕 x 轴转动惯量/（kg·m2） 1 030 悬浮模块绕 y 轴转动惯量/（kg·m2） 1 800 悬浮模块绕 z 轴转动惯量/（kg·m2） 2 680 二系悬挂弹簧纵向刚度/（N·m−1） 900 000 二系悬挂弹簧竖向刚度/（N·m−1） 80 000 二系悬挂弹簧横向刚度/（N·m−1） 80 000 二系悬挂弹簧纵向阻尼/（N·s·m−1） 50 000 二系悬挂弹簧竖向阻尼/（N·s·m−1） 2 000 二系悬挂弹簧横向阻尼/（N·s·m−1） 4 000 线圈匝数/匝 96 磁导率/（× 10−6 H·m−1） 1.26 铁芯极面积/m2 0.383 额定气隙/mm 8 车体长度/m 16 
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