移动荷载作用下结构与地基动力响应特性研究
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摘要
为了研究运动车辆作用下交通工程结构(铁路、公路、机场跑道等)及其周边地基的动力响应问题,本文建立了四个不同的力学分析模型分别用于分析不同的交通工程结构与地基在运动车辆作用下的动力响应,即:(ⅰ)Kelvin地基上无限长梁;(ⅱ)弹性半空间上无限长梁;(ⅲ)Kelvin地基上无限大板;(ⅳ)粘弹性半空间体。第一和第二个模型可作为铁路轨道的力学分析模型,第三个可作为公路或机场跑道等路面体系的力学分析模型,最后一个可作为地基的力学分析模型。
本文采用移动荷载来模拟运动车辆(列车、汽车、飞机等)作用于轨道或路面体系的荷载。根据其空间分布函数,将移动荷载划分为点源、线源和面源荷载,根据其时间变化函数,将移动荷载划分为恒载和简谐荷载,它们的组合构成了六种基本的移动荷载模式。除了上述单轮荷载之外,本文还分析了多轮荷载,即采用移动集中荷载列模拟了列车作用于轨道的荷载;采用移动矩形均布荷载阵列模拟了汽车作用于路面体系的荷载;采用移动线源非均布荷载列模拟了列车轨道作用于地基的荷载。
根据是否考虑加载、结构初始条件等因素对结构动力响应的影响,本文将结构的动力响应划分为瞬态响应和稳态响应。对于结构的瞬态响应,本文的重点在于模拟结构动力响应从瞬态过渡到稳态的全过程,以及由荷载突然施加而引起的冲击效应。对于稳态响应,本文的重点在于分析地基参数、结构参数和荷载参数等对结构稳态响应的影响。
本文采用两种方法推导了结构与地基动力响应的解析解,即Green函数法和直接积分变换法。在Green函数法中,本文首先证明了可用于求解任意动荷载作用下结构与地基动力响应的广义Duhamel积分,通过广义Duhamel积分将移动源产生的物理场用固定源产生的物理场(Green函数)表达。至于Green函数本身的求解,本文则采用积分变换法导出了其解析解。Green函数法是求解该类问题的一个统一有效的普遍方法,贯穿了论文的始末,建立了各个子问题的联系。然而,虽然Green函数法是一个统一有效的普遍方法,但对于具体问题而言,它往往并不是最简单、最直接的方法。因此,本文还采用直接积分变换法推导了结构与地基动力响应的解析解,与Green函数法相比,直接积分变换法往往更简单。但是,Greed函数法的优势突出表现为它将解析法
To study the traffic induced structure borne and ground borne vibrations, four types of structures and ground were formulated to model the railway track and highway or runway pavement system, including (i) infinite beam on Kelvin foundation, (ii) infinite beam on an elastic half-space, (iii) infinite plate on Kelvin foundation, and (iv) a visco-elastic half-space. The first two can be used to model the railway track, the third one model the highway or runway pavement system, and the last model the ground.Moving loads were utilized to model the wheel loads and could be classified into various groups according to their spatial distribution function and temporal variation function. In terms of spatial distribution, mainly three kinds of moving loads were considered, i.e., (i) moving point source, (ii) moving line source, and (iii) moving area source. In terms of temporal variation, two kinds of moving loads were considered, including (i) constant load, and (ii) harmonic load. Besides the single wheel loads, multiple wheel loads were also studied. A seires of moving point load was utilized to model the axle loads acted on the railway track by trains, an array of moving load, each unfiromly distributed over a rectangular area, model the axle loads acted on the highway pavement system by tandem double wheel trucks, and a seires of elastically distribured moving load model loads acted on the gournd by the railway track under multiple axle loads.Two kinds of dynamic response, i.e., transient response and steady-state response, were studied for each of the four models, respectively. For transient response, focuses were mainly placed on simulating the whole process in which transient response evolve into steady-state response and the impact effects induced by suddenly applied moving loads. For steady-state response, however, focuses were mainly placed on investigating the effect of various parameters on the steady-state response.Analytical solutions of the dynamic responses were developed by two methods, i.e., Green's function method and integral transform method. For Green's function method, generalized Duhamel's integral, which is eurytopic to solve dynamic responses of linear system were presented first. Green's function for each model was then developed in the transformed field using Fourier transform and/or Laplace transform. Dynamic responses were finally expressed as convolution integrals between moving loads and Green's function. Green's function method is applicable to solve all the four models, however, it's not the
本文采用移动荷载来模拟运动车辆(列车、汽车、飞机等)作用于轨道或路面体系的荷载。根据其空间分布函数,将移动荷载划分为点源、线源和面源荷载,根据其时间变化函数,将移动荷载划分为恒载和简谐荷载,它们的组合构成了六种基本的移动荷载模式。除了上述单轮荷载之外,本文还分析了多轮荷载,即采用移动集中荷载列模拟了列车作用于轨道的荷载;采用移动矩形均布荷载阵列模拟了汽车作用于路面体系的荷载;采用移动线源非均布荷载列模拟了列车轨道作用于地基的荷载。
根据是否考虑加载、结构初始条件等因素对结构动力响应的影响,本文将结构的动力响应划分为瞬态响应和稳态响应。对于结构的瞬态响应,本文的重点在于模拟结构动力响应从瞬态过渡到稳态的全过程,以及由荷载突然施加而引起的冲击效应。对于稳态响应,本文的重点在于分析地基参数、结构参数和荷载参数等对结构稳态响应的影响。
本文采用两种方法推导了结构与地基动力响应的解析解,即Green函数法和直接积分变换法。在Green函数法中,本文首先证明了可用于求解任意动荷载作用下结构与地基动力响应的广义Duhamel积分,通过广义Duhamel积分将移动源产生的物理场用固定源产生的物理场(Green函数)表达。至于Green函数本身的求解,本文则采用积分变换法导出了其解析解。Green函数法是求解该类问题的一个统一有效的普遍方法,贯穿了论文的始末,建立了各个子问题的联系。然而,虽然Green函数法是一个统一有效的普遍方法,但对于具体问题而言,它往往并不是最简单、最直接的方法。因此,本文还采用直接积分变换法推导了结构与地基动力响应的解析解,与Green函数法相比,直接积分变换法往往更简单。但是,Greed函数法的优势突出表现为它将解析法
To study the traffic induced structure borne and ground borne vibrations, four types of structures and ground were formulated to model the railway track and highway or runway pavement system, including (i) infinite beam on Kelvin foundation, (ii) infinite beam on an elastic half-space, (iii) infinite plate on Kelvin foundation, and (iv) a visco-elastic half-space. The first two can be used to model the railway track, the third one model the highway or runway pavement system, and the last model the ground.Moving loads were utilized to model the wheel loads and could be classified into various groups according to their spatial distribution function and temporal variation function. In terms of spatial distribution, mainly three kinds of moving loads were considered, i.e., (i) moving point source, (ii) moving line source, and (iii) moving area source. In terms of temporal variation, two kinds of moving loads were considered, including (i) constant load, and (ii) harmonic load. Besides the single wheel loads, multiple wheel loads were also studied. A seires of moving point load was utilized to model the axle loads acted on the railway track by trains, an array of moving load, each unfiromly distributed over a rectangular area, model the axle loads acted on the highway pavement system by tandem double wheel trucks, and a seires of elastically distribured moving load model loads acted on the gournd by the railway track under multiple axle loads.Two kinds of dynamic response, i.e., transient response and steady-state response, were studied for each of the four models, respectively. For transient response, focuses were mainly placed on simulating the whole process in which transient response evolve into steady-state response and the impact effects induced by suddenly applied moving loads. For steady-state response, however, focuses were mainly placed on investigating the effect of various parameters on the steady-state response.Analytical solutions of the dynamic responses were developed by two methods, i.e., Green's function method and integral transform method. For Green's function method, generalized Duhamel's integral, which is eurytopic to solve dynamic responses of linear system were presented first. Green's function for each model was then developed in the transformed field using Fourier transform and/or Laplace transform. Dynamic responses were finally expressed as convolution integrals between moving loads and Green's function. Green's function method is applicable to solve all the four models, however, it's not the
引文
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[2] 沙庆林.高速公路沥青路面早期破坏现象及预防.北京:人民交通出版社,2001.
[3] Japanese Institute of Noise Control. Regional Vibration of Environments. Tokyo: Jibaotang Press, 2001.
[4] L. Auersch. Zur entsehung und ausbreitung von schienenverkehrserchutterungen-theoreische untersuchungen und messungen an hochgeschwindigkeitszug intercity experimental. Forschungsbericht 155, Bundesanstalt fur Materialforschung und—prfung, Berlin, 1999.
[5] J. Branderhorstllen. Modellen vooor het boeggolfprobleem bij hogesnelheidstreinen. Ontwerp en validatie met behulp van de resultaen van de proef Amsterdam-Utrecht. Universiteit Twente, Holland Railconsult, 1997.
[6] G. Degrande and L. Schillemans. Free field vibrations during the passage of a HST. Proceedings of IMSA 23, Noise and Vibration Engineering, P. Sas (editor), Leuven, Belgium, 1998: 1563-1570.
[7] G. Degrande. Free field vibrations during the passage of a high speed train: experimental results and numerical predictions. Noise and Vibaration from High-speed Trains, V. V. Krylov (editor). London, Telford Publishsing, 2000: 1-28.
[8] G. Degrande, G. Lombaert. High speed train induced field vibrations: in situ measurements and numerical modeling. Proceedings of the International Workshop Wave 2000, Wave 2000, Nawawi Chouw and Gunther Schmid (editors), Bochum, Germany, 2000: 29-41.
[9] 孙璐.运动车辆随机荷载及其激励下地面的动力响应的理论研究.东南大学,1996.
[10] 周云.交通荷载对周边建筑的振动影响分析.浙江大学,2005.
[11] 左迎辉.移动荷载作用下饱和土体的动力响应.浙江大学,2005.
[12] 夏禾、曹艳梅.轨道交通引起的环境振动问题.铁道科学与工程学报,2004,1(1):44-51.
[13] 张楠、夏禾.地铁列车对临近建筑物振动影响的研究.工程力学(增刊),2001,199-203.
[14] D. V. Jones and M. Petyt. Ground vibration in the vicinity of a strip load: a two-dimensional halfspace model. Journal of Sound and Vibration, 1991, 147(1): 155-166.
[15] D. V. Jones and M. Petyt. Ground vibration in the vicinity of a strip load: an elastic layer on a rigid foundation. Journal of Sound and Vibration, 1992, 152(3): 501-515.
[16] D. V. Jones and M. Petyt. Ground vibration in the vicinity of a strip load: an elastic layer on an elastic half-space. Journal of Sound and Vibration, 1993, 161(1): 1-18.
[17] D. V. Jones and M. Petyt. Ground vibration in the vicinity of a rectangular load on a half-space. Journal of Sound and Vibration, 1993, 166(1): 141-159.
[18] D. V. Jones, O. Laghrouche, D. Le Houedec and M. Petyt. Ground vibration in the vicinity of a rectangular load acting on a viscoelatic layer over a rigid foundation. Journal of Sound and Vibration, 1997, 202(2): 307-319.
[19] D. V. Jones, D. Le Houedec, A. T. Peplow and M. Petyt. Ground vibration in the vicinity of a moving harmonic rectangular load on a half-space. European Journal of Mechanics, A/Solids, 1998, 17: 153-166.
[20] D. V. Jones, D. Le Houedec and M. Petyt. Ground vibrations due to a rectangular harmonic load. Journal of Sound and Vibration, 1998, 212(1): 61-74.
[21] X. Sheng, C. J. C. Jones and M. Petyt. Ground vibration generated by a harmonic load acting on a railway track. Journal of Sound and Vibration, 1999, 225(1): 3-28.
[22] X. Sheng, C. J. C. Jones and M. Petyt. Ground vibration generated by a load moving along a railway track. Journal of Sound and Vibration, 1999, 228(1): 129-156.
[23] E. Kausel and L. Tassoulas. Transmitting boundaries: a closed-form comparison. Bulletin of the Seismological Society of America, 1981, 71(1): 143-159.
[24] 廖振鹏.工程波动理论导论.北京:科学出版社,2002.
[25] R. Y. S. Pak and B. B. Guzina. Seismic soil-structure interaction analysis by direct boundary element methods. International Journal of Solids and Structures, 1999, 36: 4743-4766.
[26] M. Mohammadi and Karabalis. Dynamic 3-d soil-railway track interaction by bem-fem. Earthquake Engineering and Soil Dynamics, 1995, 24: 1177-1193.
[27] P. K. Banerjee and S. M. Mamoon. A fundamental solution due to a periodic point force in the interior of an elastic half-space. Earthquake Engineering and Structural Dynamics, 1990, 19: 91-105.
[28] P. K. N. D. Rajapakse and Y. Wang. Elastodynamic Green's functions of orthotropic half plane. ASCE Journal of Engineering Mechanics, 1991, 1170): 588-603.
[29] G. B. Muravskii. Green functions for an incompressible linearly nonhomogeneous half-space. Archieve of Applied Mechanics, 1996, 67:81-95.
[30] A. Saez and J. Dominguez. BEM analysis of wave scattering in transversely isotropic solids. Inter-national Journal for Numerical Methods in Engineering, 1999, 44: 1283-1300.
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