地铁引起环境振动及房屋浮置楼板隔振研究
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摘要
近来年,一方面,由于地铁交通的大力发展,地铁距建筑物越来越近,有的就在建筑物正下方运行;另一方面,由于人们生活水平的提高、精密仪器的灵敏度和精度越来越高,对振动的限制越来越严格。因此,地铁引起环境振动问题越来越突出,研究地铁引起环境振动及隔振问题具有重要的理论意义和工程应用价值。本文结合同济大学建筑设计研究院设计的上海音乐学院拟建项目,对地铁引起环境振动及房屋浮置楼板隔振等若干问题进行了研究,主要包括以下几个方面的内容:
1.振动对环境特别是对人的影响,不仅与振动强度大小有关,而且与振动的频率、方向和暴露时间等有关,因此,研究了由加速度时程,获得其对应分频值,即1/3倍频程中心频率对应加速度值的方法。评价振动对环境的影响,必然需要一定的标准,因此系统研究了有关振动评价标准,进而提出频域内振动评价国家标准的应用方法。
2.列车运行作用在轨道上的力可分解为常值的拟静力和轮轨动接触力,前者是由于列车重量引起,后者是由于道床不均匀、轨道不平顺和车体自身振动等引起。本文采用理论方法计算列车运行引起环境振动的振源竖向振动加速度,并将计算结果与实测值进行比较分析,两者基本吻合。列车引起环境振动的振源振动主要由轮轨动接触力和轨道不平顺引起,拟静力引起的振动很小。
3.传统的振动信号分析,一般采用Fourier谱分析方法,Fourier谱分析主要适用于线性平稳信号,由于地铁列车质量和运行速度等的不确定性、振源(列车-轨道-路基系统)机理和振动传播途径(地基土等)的复杂性以及地面背景振动的干扰,地铁引起地面振动并非严格意义上的线性平稳信号。利用适用范围更宽,可用于非平稳信号分析的正交Hilbert-Huang变换,对实际量测的地铁引起地面振动信号进行分析,研究地铁引起地面振动的频谱特性,并与Fourier谱进行比较。利用Hilbert边际谱计算分析纯粹地铁引起地面振动的频谱特性。
4.基于有限元方法计算分析地铁引起地面振动及其衰减规律时,考虑土体等复杂结构,受到频率分布较广及高频振动激励,将产生复杂的拍现象。采用多个控制频率来确定阻尼比,从而使振动在整个频率范围内的阻尼比与事先确定的控制阻尼比之差满足要求,进而建立Caughey阻尼模型,利用该模型计算土体的动响应,并与按Rayleigh阻尼模型的计算结果进行比较。结果表明,按Rayleigh阻尼模型算得的系统振动响应偏小。
5.比较利用平面和空间两种模型计算框架结构房屋在地铁引起地面竖向振动作用下的响应,两模型的计算结果基本一致。为避免采用如“轨道道床-地基土-地面建筑物”等整体模型时,由于地基土的复杂性和不确定性等所带来的误差,利用容易量测的地铁运行时地铁隧道附近地面振动加速度时程,作为输入激励,计算比较在多种激励、Caughey阻尼和Rayleigh阻尼模型情况下,结构的振动响应。利用国家标准及其前述应用方法对地铁引起房屋振动进行评价,并考察行波效应和两种阻尼对计算结构振动响应的影响。
6.对于地铁引起的高频振动,由单自由度入手,计算分析钢弹簧隔振的特点。利用Caughey阻尼和Rayleigh阻尼模型计算地铁引起浮置楼板的振动响应,进而评价浮置楼板的隔振效果。
With many more subways having been completed or being planed to be constructed in recent years, on the one hand, the subway trains are running closer and closer to the residential or industrial areas, and some even go exactly under the up-ground buildings; and on the other hand, the limit on vibration level is becoming increasingly strict due to the improvement of people's living standard and the enhancement of delicate instruments' sensitivity. As a result, the problem of environmental vibration induced by underground trains has become more serious than ever before. Therefore, the further research on the subway-induced environmental vibration has important theoretical and practical application values. In this dissertation, some theoretical and numerical techniques are developed to study several aspects of the subway-induced vibration problem, benefiting from the design information provided by the Architectural Design & Research Institute of Tongji University and the measurement data performed at the site. The main contents of this study are as follows:
1. The influencing factors of which vibration impacts on environment include the vibration intensity, direction and frequency. The method of calculating acceleration RMS (root mean square) values in one-third octave frequency, by the recorded data of acceleration time history, is presented. And with this method, subway-induced environmental vibrations can be quantitatively evaluated, according to the national standard of evaluating vibration level in frequency domain.
2. The forces acting at rails are the combination of the quasistatic forces caused by the successive axle load, and the dynamic forces mainly originated by the unevenness of rails and of carriages' wheels. The accelerations of the source of environmental vibrations caused by underground trains are calculated, and the comparison of these calculated accelerations with the measured ones is made. The accelerations of the vibrational source significantly result from the dynamic forces, and the ones caused by the quasistatic forces can be neglected.
3. Although Fourier spectral analysis provides a general method for examining signals' frequency property, there are some crucial restrictions of the Fourier spectral analysis: the system must be linear; and the signals must be strictly stationary. However, the subway-induced ground vibration signals are not strictly-defined linear stationary signals, because of the complexity of the mechanism of the subway-induced vibration source and transmitting media, the diversification of train's loads and speeds, and the interaction of background vibrations. The frequency spectrum properties of the measured subway-induced ground vibrations are analyzed based on the orthogonal Hilbert-Hung Transform which is ideal for nonlinear and non-stationary signal analysis. The spectral properties of the subway-induced ground vibrations eliminating background ones are displayed by the investigation of the marginal Hilbert spectra of the data.
4. The complex beat phenomena occur in soil or other complicated structures subjected to the excitation with wide range of frequencies. Based on the thorough examination of the damping ratio-frequency relation, the Caughey damping model, of calculating the damping of the system excited by vibrations with wide range of frequencies, is built. According to the Caughey damping model, the dynamic response analysis of soil under the action of subway-induced vibrations is made, based on the dynamic finite element method, and the results are greater than those obtained by the Rayleigh damping method.
5. The comparison is made, of the dynamic responses analyzed by two-dimension and three-dimension model of the same frame structure building under the subway-induced vibration excitation, and there is little difference between the two results calculated with the two models. Therefore, Two-dimensional finite element model is developed, using the results cf a ground vibration measurement campaign purposely performed at the site as input excitations. Based on the Caughey and Rayleigh damping model, the vibration levels in the structure are calculated respectively, to multi-support, traveling wave and uniform excitation, and the comparison of the vibration levels is made. The quantitative evaluation of the vibration levels is made based on the Chinese national standard on limit of vibration, and the effects of traveling wave and damping are investigated.
6. An analytical model of the single degree of freedom system of a floating floor is established. The characteristics of the spring vibration isolation are presented based on the calculation of the analytical model. The responses of the floating floor subjected to subway-induced vibrations are respectively analyzed with the Caughey and Rayleigh damping model, and the isolation efficiency of the floating floor is quantitatively evaluated.
1.振动对环境特别是对人的影响,不仅与振动强度大小有关,而且与振动的频率、方向和暴露时间等有关,因此,研究了由加速度时程,获得其对应分频值,即1/3倍频程中心频率对应加速度值的方法。评价振动对环境的影响,必然需要一定的标准,因此系统研究了有关振动评价标准,进而提出频域内振动评价国家标准的应用方法。
2.列车运行作用在轨道上的力可分解为常值的拟静力和轮轨动接触力,前者是由于列车重量引起,后者是由于道床不均匀、轨道不平顺和车体自身振动等引起。本文采用理论方法计算列车运行引起环境振动的振源竖向振动加速度,并将计算结果与实测值进行比较分析,两者基本吻合。列车引起环境振动的振源振动主要由轮轨动接触力和轨道不平顺引起,拟静力引起的振动很小。
3.传统的振动信号分析,一般采用Fourier谱分析方法,Fourier谱分析主要适用于线性平稳信号,由于地铁列车质量和运行速度等的不确定性、振源(列车-轨道-路基系统)机理和振动传播途径(地基土等)的复杂性以及地面背景振动的干扰,地铁引起地面振动并非严格意义上的线性平稳信号。利用适用范围更宽,可用于非平稳信号分析的正交Hilbert-Huang变换,对实际量测的地铁引起地面振动信号进行分析,研究地铁引起地面振动的频谱特性,并与Fourier谱进行比较。利用Hilbert边际谱计算分析纯粹地铁引起地面振动的频谱特性。
4.基于有限元方法计算分析地铁引起地面振动及其衰减规律时,考虑土体等复杂结构,受到频率分布较广及高频振动激励,将产生复杂的拍现象。采用多个控制频率来确定阻尼比,从而使振动在整个频率范围内的阻尼比与事先确定的控制阻尼比之差满足要求,进而建立Caughey阻尼模型,利用该模型计算土体的动响应,并与按Rayleigh阻尼模型的计算结果进行比较。结果表明,按Rayleigh阻尼模型算得的系统振动响应偏小。
5.比较利用平面和空间两种模型计算框架结构房屋在地铁引起地面竖向振动作用下的响应,两模型的计算结果基本一致。为避免采用如“轨道道床-地基土-地面建筑物”等整体模型时,由于地基土的复杂性和不确定性等所带来的误差,利用容易量测的地铁运行时地铁隧道附近地面振动加速度时程,作为输入激励,计算比较在多种激励、Caughey阻尼和Rayleigh阻尼模型情况下,结构的振动响应。利用国家标准及其前述应用方法对地铁引起房屋振动进行评价,并考察行波效应和两种阻尼对计算结构振动响应的影响。
6.对于地铁引起的高频振动,由单自由度入手,计算分析钢弹簧隔振的特点。利用Caughey阻尼和Rayleigh阻尼模型计算地铁引起浮置楼板的振动响应,进而评价浮置楼板的隔振效果。
With many more subways having been completed or being planed to be constructed in recent years, on the one hand, the subway trains are running closer and closer to the residential or industrial areas, and some even go exactly under the up-ground buildings; and on the other hand, the limit on vibration level is becoming increasingly strict due to the improvement of people's living standard and the enhancement of delicate instruments' sensitivity. As a result, the problem of environmental vibration induced by underground trains has become more serious than ever before. Therefore, the further research on the subway-induced environmental vibration has important theoretical and practical application values. In this dissertation, some theoretical and numerical techniques are developed to study several aspects of the subway-induced vibration problem, benefiting from the design information provided by the Architectural Design & Research Institute of Tongji University and the measurement data performed at the site. The main contents of this study are as follows:
1. The influencing factors of which vibration impacts on environment include the vibration intensity, direction and frequency. The method of calculating acceleration RMS (root mean square) values in one-third octave frequency, by the recorded data of acceleration time history, is presented. And with this method, subway-induced environmental vibrations can be quantitatively evaluated, according to the national standard of evaluating vibration level in frequency domain.
2. The forces acting at rails are the combination of the quasistatic forces caused by the successive axle load, and the dynamic forces mainly originated by the unevenness of rails and of carriages' wheels. The accelerations of the source of environmental vibrations caused by underground trains are calculated, and the comparison of these calculated accelerations with the measured ones is made. The accelerations of the vibrational source significantly result from the dynamic forces, and the ones caused by the quasistatic forces can be neglected.
3. Although Fourier spectral analysis provides a general method for examining signals' frequency property, there are some crucial restrictions of the Fourier spectral analysis: the system must be linear; and the signals must be strictly stationary. However, the subway-induced ground vibration signals are not strictly-defined linear stationary signals, because of the complexity of the mechanism of the subway-induced vibration source and transmitting media, the diversification of train's loads and speeds, and the interaction of background vibrations. The frequency spectrum properties of the measured subway-induced ground vibrations are analyzed based on the orthogonal Hilbert-Hung Transform which is ideal for nonlinear and non-stationary signal analysis. The spectral properties of the subway-induced ground vibrations eliminating background ones are displayed by the investigation of the marginal Hilbert spectra of the data.
4. The complex beat phenomena occur in soil or other complicated structures subjected to the excitation with wide range of frequencies. Based on the thorough examination of the damping ratio-frequency relation, the Caughey damping model, of calculating the damping of the system excited by vibrations with wide range of frequencies, is built. According to the Caughey damping model, the dynamic response analysis of soil under the action of subway-induced vibrations is made, based on the dynamic finite element method, and the results are greater than those obtained by the Rayleigh damping method.
5. The comparison is made, of the dynamic responses analyzed by two-dimension and three-dimension model of the same frame structure building under the subway-induced vibration excitation, and there is little difference between the two results calculated with the two models. Therefore, Two-dimensional finite element model is developed, using the results cf a ground vibration measurement campaign purposely performed at the site as input excitations. Based on the Caughey and Rayleigh damping model, the vibration levels in the structure are calculated respectively, to multi-support, traveling wave and uniform excitation, and the comparison of the vibration levels is made. The quantitative evaluation of the vibration levels is made based on the Chinese national standard on limit of vibration, and the effects of traveling wave and damping are investigated.
6. An analytical model of the single degree of freedom system of a floating floor is established. The characteristics of the spring vibration isolation are presented based on the calculation of the analytical model. The responses of the floating floor subjected to subway-induced vibrations are respectively analyzed with the Caughey and Rayleigh damping model, and the isolation efficiency of the floating floor is quantitatively evaluated.
引文
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