轨道结构在移动荷载作用下的周期解析解
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摘要
为研究列车振动在地表的传播规律,推导了轨道结构在移动荷载作用下动力响应的解析解形式。文中首先以Duhamel积分为基础,应用动力互等定理,得到了移动荷载作用下,半无限弹性空间体上任意点的动力响应的一般表达式;然后在该式的基础上,针对轨道结构的周期性特点,将荷载沿钢轨的移动问题转化为拾振点以L为周期向反方向跳跃式移动与荷载只在一个轨枕间距L内移动的组合移动问题。以此,将一个从-∞到+∞的积分问题转化为了任意点频域周期解析的叠加问题,从而得到了轨道结构在移动荷载作用下动力响应的新的解析解形式。
In order to study the dynamic response of the ground due to the moving trains on the railway, a new dynamic periodic close form solution is introduced for the railway structure subjected to moving loads in this paper. Firstly, the general dynamical response in a elastic half space model subjected to the surface moving loads is obtained on the basis of Duhamel integral and dynamic reciprocity theorem. Secondly, in the case of periodic railway track structure, the general dynamical response in frequency domain is simplified in a form of summation within the track sleeper period instead of integral from -∞ to +∞, which is obtained by transferring the moving loads on the rail to the moving of receiver backward within periodic sleeper distance. The advantage of this formulation is that all the dynamical analysis of the track system is carried out within sleeper distance. In this way, the ground response by the moving train can be obtained by a very simple calculation program.
In order to study the dynamic response of the ground due to the moving trains on the railway, a new dynamic periodic close form solution is introduced for the railway structure subjected to moving loads in this paper. Firstly, the general dynamical response in a elastic half space model subjected to the surface moving loads is obtained on the basis of Duhamel integral and dynamic reciprocity theorem. Secondly, in the case of periodic railway track structure, the general dynamical response in frequency domain is simplified in a form of summation within the track sleeper period instead of integral from -∞ to +∞, which is obtained by transferring the moving loads on the rail to the moving of receiver backward within periodic sleeper distance. The advantage of this formulation is that all the dynamical analysis of the track system is carried out within sleeper distance. In this way, the ground response by the moving train can be obtained by a very simple calculation program.
引文
[1]雷晓燕.铁路轨道结构数值分析方法[M].北京:中国铁道出版社,1998.LeiXiaoyan.Numerical analysis method for railway track structures[M].Beijing:ChinaRailwayPublishingCompany,1998.(inChinese)
[2]JonesC J C.Simulations of ground vibration from a moving harmonic load on a railway track[J].Journal ofSound andVibration,2000,231(3):739-751.
[3]ShamaltaM.Analytical study of dynamic response of an embedded railway track to moving load[J].Archive ofAppliedMechanics,2003,73(1-2):131-146.
[4]陶连金.地铁诱发地面运动衰减规律的研究分析[J].世界地震工程,2003,19(1):83-87.TaoLianjin.Study of aHenuation law of ground motion induced by subway shock[J].WorldEarthquakeEngineering,2003,19(1):83-87.(inChinese)
[5]JonesC J C.A model for ground vibration from railway tunnels[J].Proceedings of theInstitution ofCivilEngineeringTransport,2002,153(2):121-129.
[6]PicouxB.Propagation of vibrations from a railway track lying on a semi-infinite soft ground[J].Proceedings of the eightInteractionConference onCivil andStructuralEngineeringCompacting,2001.279-280.
[7]L Fryba.Vibration of solids and structures under moving loads[M].NoordhoffInternationalPublishing,1999.
[8]C R Steele.TheFinite beam with a movingLoad[J].J.Appl.Mech.,1997,35(4):111-119.
[9]邓学钧.车辆--地面结构系统动力学[M].北京:人民交通出版社,2000.DengXuejun.Dynamic analysis of vehicle-ground structure systems[M].Beijing:PeoplesCommunicationPress,2000.(inChinese)
[10]孙璐.匀速运动的线源荷载激励下无限长梁动力分析[J].应用数学和力学,1998,19(4):341-347.SunLu.Dynamic analysis of infinite beam under a moving line load with uniform velocity[J].AppliedMathematics andMechanics,1998,19(4):341-347.(inChinese)
[2]JonesC J C.Simulations of ground vibration from a moving harmonic load on a railway track[J].Journal ofSound andVibration,2000,231(3):739-751.
[3]ShamaltaM.Analytical study of dynamic response of an embedded railway track to moving load[J].Archive ofAppliedMechanics,2003,73(1-2):131-146.
[4]陶连金.地铁诱发地面运动衰减规律的研究分析[J].世界地震工程,2003,19(1):83-87.TaoLianjin.Study of aHenuation law of ground motion induced by subway shock[J].WorldEarthquakeEngineering,2003,19(1):83-87.(inChinese)
[5]JonesC J C.A model for ground vibration from railway tunnels[J].Proceedings of theInstitution ofCivilEngineeringTransport,2002,153(2):121-129.
[6]PicouxB.Propagation of vibrations from a railway track lying on a semi-infinite soft ground[J].Proceedings of the eightInteractionConference onCivil andStructuralEngineeringCompacting,2001.279-280.
[7]L Fryba.Vibration of solids and structures under moving loads[M].NoordhoffInternationalPublishing,1999.
[8]C R Steele.TheFinite beam with a movingLoad[J].J.Appl.Mech.,1997,35(4):111-119.
[9]邓学钧.车辆--地面结构系统动力学[M].北京:人民交通出版社,2000.DengXuejun.Dynamic analysis of vehicle-ground structure systems[M].Beijing:PeoplesCommunicationPress,2000.(inChinese)
[10]孙璐.匀速运动的线源荷载激励下无限长梁动力分析[J].应用数学和力学,1998,19(4):341-347.SunLu.Dynamic analysis of infinite beam under a moving line load with uniform velocity[J].AppliedMathematics andMechanics,1998,19(4):341-347.(inChinese)
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