移动荷载作用下轨道基础刚度突变对轨道振动的影响
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摘要
通过建立移动荷载作用下具有基础弹性刚度突变连续梁的振动微分方程,得到了梁的变形解析表达式。利用该解析解和叠加原理,以车辆通过铁路轨道为例,研究了轨道基础弹性突变对轨道振动的影响,分析了单轮对和一台TGV高速动车通过五种轨道刚度比时的轨道动力响应。计算表明,基础弹性突变对梁的振动有较大影响,其影响随着移动荷载速度的增加而增加。
Analytical deformation formula of the continuous beam under moving loads has been derived by establishing the vibration differential equation of the continuous beam with foundation elasticity stiffness abrupt change.Taking the railway track as an example,the effect of the abrupt change of the track foundation elasticity stiffness on track vibration is investigated and the dynamic responses of the track under a single wheel set and a TGV high speed locomotive when passing through the track with five stiffness ratios are analyzed by means of this formula and the superposition principle.The computations show that the foundation elasticity stiffness abrupt change has greater influences on beam vibration.This influences increase with increase of the velocity of the moving loads.
Analytical deformation formula of the continuous beam under moving loads has been derived by establishing the vibration differential equation of the continuous beam with foundation elasticity stiffness abrupt change.Taking the railway track as an example,the effect of the abrupt change of the track foundation elasticity stiffness on track vibration is investigated and the dynamic responses of the track under a single wheel set and a TGV high speed locomotive when passing through the track with five stiffness ratios are analyzed by means of this formula and the superposition principle.The computations show that the foundation elasticity stiffness abrupt change has greater influences on beam vibration.This influences increase with increase of the velocity of the moving loads.
引文
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[2]K err A D.A m ethod for determ in ing the track m odu-lus us ing a locom otive or car on m u lti-ax le trucks[A].P roceed ing Am erican R a ilw ay Eng ineering A ssoc iation[C].1987,84(2):270—286.
[3]K err A D.O n the vertica l m odu lus in the standardra ilw ay track ana lyses[J].R a il In ternationa l,1989,235(2):37—45.
[4]N am ura A k ira,M atsuo K o ich iro,M iura Sh igeru.In-troduction of bu ffers in to a trans itiona l track stiffnessreg ion[R].RTR I R eport,1997,11(2):39—42.
[5]柳下尚道.侨台裹盛土の沈下による轨道变形に关する理论计算[J].铁研速报,1985,A-85-119.
[6]三浦重,古贺彻志.地震时の侨台裹盛土沈下所における轨道变形と走行安全[J].铁研速报,1987,A-87-64.
[7]M oroney B E.A study of ra ilroad track trans itionpo in ts and prob lem s[D].D epartm en t of C iv il Eng i-neering,U n ivers ity of D e law are,1991.
[8]L e i X,M ao L.D ynam ic response ana lyses of veh icleand track coup led system on track trans ition of con-ven tiona l h igh speed ra ilw ay[J].Journa l of Sound andV ibration,2004,271(3):1 133—1 146.
[9]B e lzer A I.A coustics of so lids[M].Springer-V er-lag,B erlin,1988.
[10]V es ic A S.B eam s on e lastic subgrade and theW ink lerhypothes is[A].P roceed ings 5thIn t.Con f so il M ech.Found.Engng[C].Paris,1963,1:845—850.
[11]H ee lis M E,Co llop A C,D aw son A R,et a l.T ran-s ien t effects of h igh speed tra ins cross ing soft so il[A].G eotechn ica l Eng ineering for transportation In-frastructure[C].B arends et a l.(eds),B a lkem a,R ot-terdam,1999:1 809-1 814.
[12]雷晓燕.轨道力学与工程新方法[M].北京:中国铁道出版社,2002.
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