论数值分析地铁列车振动对周边环境的影响(英文版).pdf

March 8, 200721:35WSPC/165-IJSSD00220 International Journal of Structural Stability and Dynamics Vol. 7, No. 1 (2007) 151–166 c ? World Scientifi c Publishing Company NUMERICAL ANALYSIS OF VIBRATION EFFECTS OF METRO TRAINS ON SURROUNDING ENVIRONMENT H. XIA∗, Y. M. CAO and N. ZHANG School of Civil Engineering tunnel;track;dynamicinteraction;vibration;ground; environment. 1. Introduction With the growing concentration of population in metropolitan areas, the infl uence of train-induced vibrations on the environment has received great attention from the residents, and is now regarded as one of the seven main environmental prob- lems in the world. In recent years, the requirement of considering the environmental infl uence in planning and designing traffi c systems has become an essential issue. In the past, the cities were small and the buildings were relatively sparse, thus traffi c- induced vibration was not considered as a serious environmental problem. While at present, with the rapid growth of modern large cities, the metro lines, urban rail- ways and elevated traffi c roads have gradually formed a multi-dimensional traffi c system, extending and intruding from the underground, ground and overhead into the crowded residential areas, commercial centers and even cultural and high-tech research zones.1,2 At the same time, the traffi c fl ows are getting more intense, traffi c loads becoming heavier, and traffi c vehicles running faster. These cause the infl u- ences of traffi c-induced vibrations on the environment to be more and more serious 151 March 8, 200721:35WSPC/165-IJSSD00220 152H. Xia, Y. M. Cao and the three-dimensional track-tunnel-ground model, by which the ground vibration properties are obtained. 2. Simulation of Train Loads by Train-Track Interaction Model 2.1. Interaction model of train-track system The dynamic interaction analysis model of the train-track system is the composition of the vehicle model, the track model and the wheel-rail contact relation model. March 8, 200721:35WSPC/165-IJSSD00220 154H. Xia, Y. M. Cao Zwj(t) the wheel displacement; v(x,t) the rail defl ection at the wheel-rail contact point; δ(x) the wheel or rail profi le change; and kH the Hertzian contact coeffi cient. Based on the above assumptions, the train-track vibration system model can be established as shown in Fig. 2. The dynamic equations of equilibrium for this system can be expressed as:                                           M10···0 0M2···0 ············ 00···MNv               ¨ Z1 ¨ Z2 ··· ¨ ZNv          +      C10···0 0C2···0 00···0 00···Cv               ˙ Z1 ˙ Z2 ··· ˙ ZNv          +      K10···0 0K2···0 ············ 00···KNv               Z1 Z2 ··· ZNv          =          F1 F2 ··· FNv          Mr{¨ vr} + Cr{˙ vr} + Kr{vr} = {Fr} ,(2) where Nvis the number of vehicles considered; and Miis the diagonal mass matrix of the ith vehicle: Mi= Diag[McJcMt1Jt1Mt2Jt2Mw1Mw2···Mw4].(3) March 8, 200721:35WSPC/165-IJSSD00220 156H. Xia, Y. M. Cao l is the half distance between the two bogies of a vehicle, and a the half distance between the two wheelsets of a bogie. In Eq. (2), ¨ Zi, ˙ Ziand Zidenote respectively the acceleration, velocity and displacement vectors of the ith vehicle, with Z = ?ZcϕcZt1ϕt1Zt2ϕt2Zw1Zw2···Zw4?T.(6) Fidenotes the external force vector of the ith vehicle excited by the track movement and the rail irregularities: Fi= ?000000Fw1Fw2···Fw4?T,(7) where Fwj is defi ned according to Eq. (1) as: Fwj= kH ? Zwj− +1 ? l=−1 φn+lvj n+l− Zs(xij) ?1.5 .(8) Here vj n+l represents the nodal displacements of the rail close to the position of the jth wheel on the rail; φn+lis the interpolating function value of the (n+l)th node of the rail, related to the jth wheel; and Zs{xij } the irregularity profi le of the rail at the position of the jth wheel. March 8, 200721:35WSPC/165-IJSSD00220 Numerical Analysis of Vibration Eff ects of Metro Trains157 Also, {¨ v}, {˙ v} and {v} denote respectively the acceleration, velocity and dis- placement vectors of the rail nodes, which are the same as those used in conven- tional fi nite element dynamic equations, and {Fr} denotes the external force vector induced by the moving vehicle load, rail irregularities and the track movement: {Fr} = ?Fr1Fr2···Frn···FrN?T,(9) where Frnis the external force vector of the nth rail node, which consists of the moment and vertical forces induced by the wheel loads: Frn= ? j ? φM njF ? wj φQ njF ? wj ,(10) F? wj = kH ? Zwj− +1 ? l=−1 φn+lvj n+l− Zs(xij) ?1.5 + ?M ci 4 + Mti 2 + mwj ? · g.(11) Here φM nj and φQ nj denote respectively the rotational and vertical interpolating func- tion values of the nth node of the rail, related to the jth wheel; and g is the gravity acceleration. Equation (2) is composed of simultaneous diff erential equations of the track and the moving vehicles. Since φM nj, φ Q nj an。