多振源激励下铁路枢纽站房结构振动响应分析与实测
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摘要
随着经济水平的快速提高，近十几年内我国建设了一大批现代化大型铁路枢纽车站。为实现铁路、地铁、轻轨以及公交等多种交通方式“零距离或短距离换乘”，多层立体式站房结构体系被广泛采用，导致人行、列车行驶和设备运行等多种振源激励同时作用在站房结构上，将对结构的正常使用功能产生较大的不利影响。因此，系统研究多振源激励下铁路枢纽站房结构的振动响应，对今后站房类结构的设计和振动控制具有十分重要的理论和实际意义。
本文以京沪线铁路枢纽车站天津西站站房结构为研究对象，对人行和列车行驶随机激励模型及应用、多振源激励的组合以及多振源激励下结构振动响应分析方法进行了系统研究，主要完成了以下五方面的工作：
（1）为准确描述行人间人行激励的差异性和单人激励各相似周期的差异性，基于Zivanovic模型提取人行激励时程标准周期曲线，通过非线性最小二乘拟合，并考虑单人激励各周期、幅值和冲量的随机特性，提出了改进的人行随机激励模型；与已有常用人行激励模型比较表明，改进模型能更有效地模拟人行激励的时域、频域特性，与实测时程更加吻合；以天津西站站房结构为研究对象，将人体等效为双自由度质量弹簧阻尼系统，建立人—结构耦合动力平衡方程，采用逐步积分法数值模拟得到人行随机激励下的结构振动响应，结果表明采用改进的人行随机激励模型分析得到的结构振动响应频域分布更宽，且激励的高频成分对结构振动有一定贡献，与实测结果更为吻合；考虑人—结构耦合作用，将减小结构振动响应，但影响较小。
（2）根据车辆随机振动理论，考虑完整的轨道不平顺功率谱和轮对间轨道输入相关性，模拟得到列车各轮对轨道不平顺位移时程，采用MATLAB软件编写程序得到二系悬挂十自由度列车系统分析模型的状态控制方程，求解得到作用在各轮对的列车行驶随机激励时程；通过与已有实测数据和模拟时程对比，验证了所得激励时程在时域、频域的合理性；对列车行驶随机激励下的天津西站站房结构振动响应进行数值模拟和实测分析，结果表明在所提出的列车行驶随机激励模型作用下，站房结构振动响应的时域、频域特性与实测结果吻合较好，候车厅层振动卓越频率位于人体对竖向振动的最敏感频率范围，应注意对人体舒适度的影响。
（3）分析研究了铁路枢纽站房结构多振源激励的组合问题，以人行和列车行驶随机激励为例，考虑到站旅客数量概率分布模型、列车满载情况以及列车行驶速度的变化，采用概率法和Monte-Carlo模拟方法得到结构设计基准期内车站人行随机激励幅值和列车行驶随机激励幅值的概率分布；根据组合激励幅值的概率特点，以2参数极值I型描述人行激励和列车行驶激励组合幅值随机变量的概率分布，确定了具有95%保证率的激励组合系数；K-S假设检验表明所提出的极值I型概率分布估计与Monte-Carlo模拟方法得到的经验概率分布结果吻合良好。
（4）通过分析人行、列车行驶和设备运行三振源单独激励下站房结构振动响应的时域、频域特性和频带交叠情况，提出了一种基于均方根加速度RMS、考虑加权功率相干叠加的多振源激励下站房结构振动响应分析方法，并对该方法的合理性和适用性进行了论证；分别采用直接叠加法和所提出的加权功率相干叠加方法进行三振源共同激励下站房结构振动响应分析，结果表明考虑加权功率相干叠加的结构振动响应均方根加速度RMS区间可以很好地包络直接叠加得到的振动响应均方根加速度RMS值；分别采用直接叠加法和考虑频域交叠的加权功率相干叠加方法对随机激励作用下结构的振动响应进行时域、频域分析，得到了三振源单独激励下站房结构振动响应之间的相干叠加效应对站房结构振动总响应的影响规律。
（5）通过人行、列车行驶和设备运行激励下下天津西站站房结构振动响应实测，得到站房轨道层及候车厅层测点的振动加速度时程，从频谱分析和RMS评价两方面分析研究了人行、列车行驶和设备运行三振源单独激励下站房结构振动响应之间的相干叠加效应对多振源激励下结构振动总响应的影响规律，并与数值模拟结果进行对比验证，结果表明加权功率相干叠加方法能很好地给出多振源激励下结构振动响应的RMS区间，且随着与振源距离的增加，包络效果更好。
With the rapid development of economy, in the past decade, a large number ofmodern railway hub stations have been built in our country. In order to realize“zero-distance or short-distance transfer” among railway, subway, light railway andbus, spatial multiple-layer structural systems are widely adopted in practice. Therefore,the structural systems have been excited simultaneously by multiple-sourceexcitations including human walking, train moving and equipment operating. Thiswill significantly affect the service and performance of the station buildings.Therefore, it is of theoretical and practical significance to study the dynamicalresponses of railway hub station buildings under multiple-source excitations in thedesign and vibration control.
Focusing on the Tianjin West Railway Station building, this dissertationsystematically studies the random excitation models of human walking and trainmoving and their applications, the combination problem of multiple-sourceexcitations and the analytical approach on the dynamical responses of railway hubstation buildings under multiple-source excitations. The main research work includesthe following assignments:
(1) An improved stochastic walking excitation model considering variations ofperiods, amplitudes and impulses is proposed to accurately describe the individualdifference of walking excitation among pedestrians and the similar cycle difference ofa single walking time histories. The normalized cycle curve of walking excitation isextracted based on Zivanovic model and optimized using non-linear least-squarecurve fit method. The improved model is verified superior to conventional models forsimulating both the time and frequency characteristics of walking excitations, andagrees well with the real measured time histories. Focusing on the Tianjin WestRailway Station building, human body is equivalent to be a mass-spring-dampermodel with two degrees of freedom. The human-structure coupled dynamic equationsare established using the improved model, and the pedestrian-induced structuralvibration responses are simulated by direct integration method. The results indicatethat, by employing the improved model, the frequency distribution of the structuralresponses is wilder and the high frequency excitation components obtained throughthe model has non-negligible effect on the structural responses, which agrees well with the measured data. In addition, the coupled effect between human and structurereduces the structural responses, but with little impact.
(2) A ten-degree secondary suspension train model is established in term of thetheory of vehicle random vibration. The intact track irregularities and correlationamong wheels on rails are considered, and the displacement time histories of eachwheel set on rail are simulated. The MATLAB program is implemented to obtain thestate governing equation of the ten-degree secondary suspension train model. Thetrain random excitation time histories are finally obtained from the state equations.The effectiveness of the train model is verified in both time and frequency domain bycomparing with measured data and several other train moving models. The dynamicalresponses of the Tianjin West Railway Station building under train moving randomexcitation are simulated and measured. The results indicate that the time andfrequency characteristics of simulated dynamical responses agree well with theexperimental data. The predominant frequency of the waiting hall is at the mostsensitive frequency band of human body during vertical vibration, and the humancomfort should be considered.
(3) The combination problem of multiple-source excitations acting on railwayhub station buildings is investigated by considering stochastic walking excitation andtrain moving random excitation. Probabilistic method and Monte-Carlo simulation areadopted to obtain the probability distributions of the extreme value of the two kinds ofexcitations during structural design duration. The study considers the probabilitycharacteristic of combined excitations and introduces The Extreme I Distribution withtwo parameters to describe the probabilistic properties of the extreme value of thecombined excitations. The combination coefficients are determined, which have aguarantee rate of95%. The K-S test shows that the probability characteristics of thecombined excitations are well evaluated by the Extreme I Distribution compared withthe empirical distribution given by Monte-Carlo simulation.
(4) Considering the frequency overlap among structural responses under eachexcitation including human walking, train moving and equipment operating, aweighted power coherent superposition method, which is based on Root Mean Square(RMS) of acceleration, is proposed for the dynamical responses of station buildingsunder multiple-source excitations. The rationality and applicability of the weightedpower coherent superposition method are also discussed. The proposed method anddirect superposition method are both adopted in the dynamical analysis of the station buildings simultaneously excited by the three excitation sources. The results indicatethat the RMS interval of structural responses calculated by the proposed method canproperly envelope the RMS value of acceleration by the direct superposition method.The direct superposition method and the proposed method are also used to analyze thedynamical responses of the station buildings excited by random vibrations both intime domain and in frequency domain. The overall responses of the station buildingare obtained in terms of the interacting superposition effects on the station buildingdue to the individual excitation.
(5) The acceleration time histories of measure points on the waiting hall andplatform layer are obtained through the measuring experiments on the Tianjin WestRailway Station under multiple-source excitations. Spectral analysis and RMSevaluation are both introduced to analyze the effects of power coherent superpositionto the overall dynamical responses with respect to human walking, train moving andequipment operating. The measured data is also compared with the numerical ones.The results show that the RMS interval of structural responses is well calculated bythe weighted power coherent superposition method. The agreement will be betterwhen the distance to excitation sources increases.
本文以京沪线铁路枢纽车站天津西站站房结构为研究对象，对人行和列车行驶随机激励模型及应用、多振源激励的组合以及多振源激励下结构振动响应分析方法进行了系统研究，主要完成了以下五方面的工作：
（1）为准确描述行人间人行激励的差异性和单人激励各相似周期的差异性，基于Zivanovic模型提取人行激励时程标准周期曲线，通过非线性最小二乘拟合，并考虑单人激励各周期、幅值和冲量的随机特性，提出了改进的人行随机激励模型；与已有常用人行激励模型比较表明，改进模型能更有效地模拟人行激励的时域、频域特性，与实测时程更加吻合；以天津西站站房结构为研究对象，将人体等效为双自由度质量弹簧阻尼系统，建立人—结构耦合动力平衡方程，采用逐步积分法数值模拟得到人行随机激励下的结构振动响应，结果表明采用改进的人行随机激励模型分析得到的结构振动响应频域分布更宽，且激励的高频成分对结构振动有一定贡献，与实测结果更为吻合；考虑人—结构耦合作用，将减小结构振动响应，但影响较小。
（2）根据车辆随机振动理论，考虑完整的轨道不平顺功率谱和轮对间轨道输入相关性，模拟得到列车各轮对轨道不平顺位移时程，采用MATLAB软件编写程序得到二系悬挂十自由度列车系统分析模型的状态控制方程，求解得到作用在各轮对的列车行驶随机激励时程；通过与已有实测数据和模拟时程对比，验证了所得激励时程在时域、频域的合理性；对列车行驶随机激励下的天津西站站房结构振动响应进行数值模拟和实测分析，结果表明在所提出的列车行驶随机激励模型作用下，站房结构振动响应的时域、频域特性与实测结果吻合较好，候车厅层振动卓越频率位于人体对竖向振动的最敏感频率范围，应注意对人体舒适度的影响。
（3）分析研究了铁路枢纽站房结构多振源激励的组合问题，以人行和列车行驶随机激励为例，考虑到站旅客数量概率分布模型、列车满载情况以及列车行驶速度的变化，采用概率法和Monte-Carlo模拟方法得到结构设计基准期内车站人行随机激励幅值和列车行驶随机激励幅值的概率分布；根据组合激励幅值的概率特点，以2参数极值I型描述人行激励和列车行驶激励组合幅值随机变量的概率分布，确定了具有95%保证率的激励组合系数；K-S假设检验表明所提出的极值I型概率分布估计与Monte-Carlo模拟方法得到的经验概率分布结果吻合良好。
（4）通过分析人行、列车行驶和设备运行三振源单独激励下站房结构振动响应的时域、频域特性和频带交叠情况，提出了一种基于均方根加速度RMS、考虑加权功率相干叠加的多振源激励下站房结构振动响应分析方法，并对该方法的合理性和适用性进行了论证；分别采用直接叠加法和所提出的加权功率相干叠加方法进行三振源共同激励下站房结构振动响应分析，结果表明考虑加权功率相干叠加的结构振动响应均方根加速度RMS区间可以很好地包络直接叠加得到的振动响应均方根加速度RMS值；分别采用直接叠加法和考虑频域交叠的加权功率相干叠加方法对随机激励作用下结构的振动响应进行时域、频域分析，得到了三振源单独激励下站房结构振动响应之间的相干叠加效应对站房结构振动总响应的影响规律。
（5）通过人行、列车行驶和设备运行激励下下天津西站站房结构振动响应实测，得到站房轨道层及候车厅层测点的振动加速度时程，从频谱分析和RMS评价两方面分析研究了人行、列车行驶和设备运行三振源单独激励下站房结构振动响应之间的相干叠加效应对多振源激励下结构振动总响应的影响规律，并与数值模拟结果进行对比验证，结果表明加权功率相干叠加方法能很好地给出多振源激励下结构振动响应的RMS区间，且随着与振源距离的增加，包络效果更好。
With the rapid development of economy, in the past decade, a large number ofmodern railway hub stations have been built in our country. In order to realize“zero-distance or short-distance transfer” among railway, subway, light railway andbus, spatial multiple-layer structural systems are widely adopted in practice. Therefore,the structural systems have been excited simultaneously by multiple-sourceexcitations including human walking, train moving and equipment operating. Thiswill significantly affect the service and performance of the station buildings.Therefore, it is of theoretical and practical significance to study the dynamicalresponses of railway hub station buildings under multiple-source excitations in thedesign and vibration control.
Focusing on the Tianjin West Railway Station building, this dissertationsystematically studies the random excitation models of human walking and trainmoving and their applications, the combination problem of multiple-sourceexcitations and the analytical approach on the dynamical responses of railway hubstation buildings under multiple-source excitations. The main research work includesthe following assignments:
(1) An improved stochastic walking excitation model considering variations ofperiods, amplitudes and impulses is proposed to accurately describe the individualdifference of walking excitation among pedestrians and the similar cycle difference ofa single walking time histories. The normalized cycle curve of walking excitation isextracted based on Zivanovic model and optimized using non-linear least-squarecurve fit method. The improved model is verified superior to conventional models forsimulating both the time and frequency characteristics of walking excitations, andagrees well with the real measured time histories. Focusing on the Tianjin WestRailway Station building, human body is equivalent to be a mass-spring-dampermodel with two degrees of freedom. The human-structure coupled dynamic equationsare established using the improved model, and the pedestrian-induced structuralvibration responses are simulated by direct integration method. The results indicatethat, by employing the improved model, the frequency distribution of the structuralresponses is wilder and the high frequency excitation components obtained throughthe model has non-negligible effect on the structural responses, which agrees well with the measured data. In addition, the coupled effect between human and structurereduces the structural responses, but with little impact.
(2) A ten-degree secondary suspension train model is established in term of thetheory of vehicle random vibration. The intact track irregularities and correlationamong wheels on rails are considered, and the displacement time histories of eachwheel set on rail are simulated. The MATLAB program is implemented to obtain thestate governing equation of the ten-degree secondary suspension train model. Thetrain random excitation time histories are finally obtained from the state equations.The effectiveness of the train model is verified in both time and frequency domain bycomparing with measured data and several other train moving models. The dynamicalresponses of the Tianjin West Railway Station building under train moving randomexcitation are simulated and measured. The results indicate that the time andfrequency characteristics of simulated dynamical responses agree well with theexperimental data. The predominant frequency of the waiting hall is at the mostsensitive frequency band of human body during vertical vibration, and the humancomfort should be considered.
(3) The combination problem of multiple-source excitations acting on railwayhub station buildings is investigated by considering stochastic walking excitation andtrain moving random excitation. Probabilistic method and Monte-Carlo simulation areadopted to obtain the probability distributions of the extreme value of the two kinds ofexcitations during structural design duration. The study considers the probabilitycharacteristic of combined excitations and introduces The Extreme I Distribution withtwo parameters to describe the probabilistic properties of the extreme value of thecombined excitations. The combination coefficients are determined, which have aguarantee rate of95%. The K-S test shows that the probability characteristics of thecombined excitations are well evaluated by the Extreme I Distribution compared withthe empirical distribution given by Monte-Carlo simulation.
(4) Considering the frequency overlap among structural responses under eachexcitation including human walking, train moving and equipment operating, aweighted power coherent superposition method, which is based on Root Mean Square(RMS) of acceleration, is proposed for the dynamical responses of station buildingsunder multiple-source excitations. The rationality and applicability of the weightedpower coherent superposition method are also discussed. The proposed method anddirect superposition method are both adopted in the dynamical analysis of the station buildings simultaneously excited by the three excitation sources. The results indicatethat the RMS interval of structural responses calculated by the proposed method canproperly envelope the RMS value of acceleration by the direct superposition method.The direct superposition method and the proposed method are also used to analyze thedynamical responses of the station buildings excited by random vibrations both intime domain and in frequency domain. The overall responses of the station buildingare obtained in terms of the interacting superposition effects on the station buildingdue to the individual excitation.
(5) The acceleration time histories of measure points on the waiting hall andplatform layer are obtained through the measuring experiments on the Tianjin WestRailway Station under multiple-source excitations. Spectral analysis and RMSevaluation are both introduced to analyze the effects of power coherent superpositionto the overall dynamical responses with respect to human walking, train moving andequipment operating. The measured data is also compared with the numerical ones.The results show that the RMS interval of structural responses is well calculated bythe weighted power coherent superposition method. The agreement will be betterwhen the distance to excitation sources increases.
引文
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