Analysis of Vibration Model and Dynamic Characteristics of the Integrated Bridge and Building Structure System for High-speed Train

Transcription

1 Analysis of Vibration Model and Dynamic Characteristics of the Integrated Bridge and Building Structure System for High-speed Train Wang Xiaoqin, Jin Wencheng, First Author School of Civil Engineering and Mechanics, Huazhong University of Science & Technology, Wuhan, Hubei, , *,Corresponding Author School of Civil Engineering and Mechanics, Huazhong University of Science & Technology, Wuhan, Hubei, Abstract In this paper, a dynamic model of the integral system structure was established based on the principle of interaction among high-speed train, rail, bridge and buildings on the bridge. Computational analysis of the model was carried out according to the station of a certain passenger dedicated line with the integrated bridge and building structure. Results revealed that the computational results of the model agreed well with measured data. When the train passed through the simple-supported beam bridge and the integrated bridge and building structure with the same span and same section at different speeds, little difference was found in the vertical displacement of the midspan of this structure. Finally, the effects of different speeds on the stability of the train body and vertical acceleration of the buildings were analyzed. Keywords: High-Speed Train, The Integrated Bridge and Building Structure, Vibration Model, Dynamic Characteristics. Introduction With the development of high-speed rail, vehicle-bridge coupling vibration has been extensively studied at home and abroad, and tremendous progress has been made. Chu K H established a vertical model of vehicle-bridge coupling [], according to a series of car models with suspension systems with eleven degrees of freedom. Bhatti M H established a truck model with twenty-three degrees of freedom and carried out the vehicle-bridge space dynamic analysis []. Li Xiaozhen divided vehicle-bridge system into two subsystems: vehicle system and bridge system, and studied the vehicle-bridge coupling vibration [3]-[5] using separate equations of motion. Academician Zeng Qingyuan has done systematic researches on vehicle-bridge vibration theory using the variational principle of potential energy of dynamics and set-in-right-position rule. All the previous studies focused on the coupling between locomotive and bridges, however, more and more new bridge-buildings combination structures appear as the result of rapid development of high-speed rail nowadays, but few researches have been done on the coupling vibration when high-speed trains pass through these structures. Literature [6] only put forward the two-step analysis method applicable to elevated stations with the integrated bridge and building structure but ignored the coupling between bridge and frame. Moreover, previous studies on coupling vibration mostly proceeded from excitation source to simulate the accuracy of locomotive motion and establish car models with different degrees of freedom, completely ignoring the effects of pier vibration on the vehicle safety as well as on the vibration of buildings on the bridge. Therefore, it is necessary to consider comprehensively by regarding high-speed rail, bridge, buildings on the bridge, pier as an interactive integral system. This paper will discuss the dynamic interactive principle of the system of high-speed rail, bridge, buildings on the bridge, establish the vibration model of the system of high-speed rail, pier, bridge and buildings on the bridge and analyze the performance of dynamic effect of the system.. Interactive model of high-speed rail, bridge, buildings on the bridge and pier When high-speed trains pass through the integrated bridge and building structure, they will exert dynamic impact to bridge structure and cause the bridge and pier to vibrate. The beam passes the force on to the pier, then to the buildings on the bridge, thus affecting the vibration of the buildings on the bridge, which, in turn, will impact the stability and comfort of the running high-speed train, the safety International Journal of Advancements in Computing Technology(IJACT) Volume5,Number6,March 03 doi:0.456/ijact.vol5.issue6.5 09

2 and comfort of the people in the buildings on the bridge, and the accuracy of the precision instrument in dispatcher s office... Car model Jg0 Mg MC JC0 C Ygh Yc Ms L ZC L Ygq L 车辆立面示意图 a) The elevation of the vehicle x Cuy x x x Kuy Cdy Kdy 4 3 Jcψ Ψgh Zgh ΨC ZC Ψgq Zgq Xgh Xc Xgq b) The top view of the vehicle and the angular displacement of the headshaking K ux Kdx C ux C dx bogie wheelset b3 b4 Train bodytrain body C dz Kdz C uz Kuz c) The schematic of the second-stage horizontal springs of the vehicle Figure. The vehicle model The establishment of the space vibration model of locomotive ignores its vertical vibration. All springs are linear. All damping is calculated as viscous damping. Creep force is considered linear. As a result, the car space vibration model is shown as follows: each wheelset has two degrees of freedom, i.e., side-sway and headshaking; each frame has four degrees of freedom, i.e., side-sway, roll, headshaking, bouncing; and five degrees of freedom: side-sway, roll, headshaking, nodding and bouncing. So, there are altogether twenty-one degrees of freedom as shown in figure. According to... M C K P, the principle of vibration and the equation of vehicle vibration, 0

3 wherem, C and K are respectively the mass matrix, damping matrix and stiffness matrix at time P is the column matrix of the load applied to the vehicle during the vibration process. t;.. Rail model Rail structure is one of the vibration elements in the big system composed of car, bridge, buildings on the bridge and pier. It is an important factor that determines the security and comfortableness of the running train. The rail mentioned in this paper adopts the Eular model and its horizontal, vertical and twist motion are discussed. The model of the rail system is shown as figure. The vertical vibration equation of the rail structure is wxyt (,, ) wxyt (,, ) wxyt (,, ) c w( x, y, t) m w( x, y, t) 4 4 x x y y k x k t n P() t ( xx ) ( y y ) i pi pi k i where w is the horizontal displacement of the rail (m); m is the mass of the unit area; c is the dumping; k is the bending stiffness; x, y are the locations of the ith concentrated load applied to the rail..3. Model of wheel-rail relationship pi pi The finite element method is used to establish the model of the wheel-rail relationship. The vertical force between the wheel and the rail is determined by the nonlinear Herts spring contact theory [7]. Z ( j, t) Z ( j, t) Z ( t) w r 0 p i G 0 The wheel and the rail becomes disconnected instantly where G is the is contact parameters of the wheel and the rail; Z ( jt, ) is the displacement of the jth wheel at time t; Z ( jt, ) is the displacement of the lower rail of the ith wheel at time t, Z () t is the r 0 boundary irregularity between the rail and the wheel. Kaller series method is used to calculate the contact tangential force between the wheel and the rail while the effects of spin creepage on lateral force and the effects of lateral creepage on creep moment are considered. Its creepage/creep force formulas are f G. abc. s T f. x x f G. abc. s T f f y y 3 x 3/ M f f f f G ab C s s 3 y 33 x, f G. 3 ab. C s 33 T is the vertical creepage; M is spin creep moment; is the vertical and lateral creepage under x, y s x, y the coordinates of contact area; s is the spin seepage; f ij is the creep coefficient; C ij is the Kaller 3/ w creep seepage; G is the shear modulus of the synthesized wheel and rail material; abare, respectively s the long and short radius of the contact ellipse..4. Model of integrated bridge and building structure Finite element model is adopted in the structure of bridge, pier and buildings on the bridge. According to different structures of specific beams, three-dimensional beam, plate element and special element are respectively used for modeling.

4 .5. Integral model With full consideration given to the structures of vehicle, rail, bridge, buildings on bridge and pier as well as mutual coupling, the dynamic interactive model of the high-speed train, rail, structure of combination of bridge and buildings is given in figure 3. Different from the vehicle-bridge vibration model studied previously, this model ) considers the instant disconnection of wheel from rail under high-speed running; ) considers the vibration of the rail structure; 3) considers the effects of the vibration of the pier on running safety and comfortableness; 4) considers the dynamic response of the buildings on the bridge and analyzes the comfortableness of the people in the buildings on the bridge. Figure. Integral Model Based on the dynamic test of the German ICE3 train passing through a certain structure of combination of bridge and buildings, the reliability of the dynamic interactive model of high-speed train, bridge, buildings on the bridge and pier is verified and analyzed. The moter car spacing of the German ICE3 train is 7.375m, the rolling diameter is 0.9m, the wheelbase of the bogie is.5m. The mass of the car body is 48,000kg, the inertial of the car body is Ix =5000kg.m, the inertia of the of the wheelset is Ix =00 kg.m, the inertia of the frame is Ix =300. Other parameters are shown in table. Distance(mm) The damper of the axle box Table. Train Geometry Size The spring of Air the axle spring box Second-stage horizontal damper Anti-hunting damper Horizontal span Center height(from the rail) Vertical span An integrated bridge and building structure adopts the form of two rail beams in two station beams and double-track single-box double-room simple-supported box girder, which is shown as figure 3. The rail structure is 7mm high, and the beam is constructed by C50 concrete. The main track is prestressed frame ballastless slab track, the steel rail is 60kg/m, the track plate is 4.8m.4m 0.9m, the elastic modulus of CA mortar is 300MPa.

5 Figure 3. Cross Section of Single Box Double Room Box Beam Figure 4 shows the comparison between the dynamic time-history curves on vertical displacement of the mid-span of simple-supported beam bridge and the integrated bridge and building structure at a speed of 00km/h, with the same span and the same single-box double-room simple beam. It can be seen from the figure that, when high-speed trains pass through simple-supported beam and the integrated bridge and building structure, the mid-span displacement increases as the train approaches and decreases as the train drives away, which is consistent with tested data and verifies the correctness of the modeling of the integral system of high-speed train, bridge, buildings on the bridge and pier. This paper also carries out a contrastive analysis of the regular pattern of the mid-span vertical displacement of the two structures at the speed of 00km/h, 50km/h and 300km/h. The results show that the dynamic response of the integrated bridge and building structure is weaker than that of simplesupported beam bridge, which is mainly due to the contribution of buildings on the bridge to the integrated bridge and building structure. a)through simple-supported beam b) Through structure of combination of bridge and buildings Figure 4. Contrast in dynamic response between the high-speed train passing through simple supported beam and through the integrated bridge and building structure Figure 5 shows the different effects on vertical displacement when the high-speed train passes through simple-supported beam bridge and structure of combination of bridge and buildings of the same span at different speeds. Data indicate that speed does not have a big impact on the vertical displacements of bridge and buildings on the bridge, but the maximum vertical displacement of the buildings on the bridge is nearly three times as much as that of the bridge. 3

6 a) Vertical displacement of the mid-span of b) Vertical displacement of the mid-span of the bridge (V=00km/h) the bridge (V=50km/h) c)vertical displacement of the mid-span of buildings on the bridge (V=00km/h) d)vertical displacement of the mid-span of buildings on the bridge (V=50km/h) Figure 5. Vertical displacements of the structures when the train passes at different speeds Figure 6 shows the contrastive analysis of the vertical acceleration of bridge mid-span and buildings on the bridge when the train passes at different speeds. Data indicate that as the speed grows, the timehistory of acceleration shows a descending trend and the maximum vertical acceleration of the buildings on the bridge is nearly one fourth as big as that of the bridge. 4

7 a) vertical acceleration of the bridge mid-span b) vertical acceleration of the bridge mid-span (V=00km/h) (V=50km/h) c)vertical acceleration of the mid-span of buildings d) vertical acceleration of the mid-span of on the bridge (V=00km/h) buildings on the bridge (V=50km/h) Figure 6. Vertical accelerations when passing through different structures at different speeds Table shows the key dynamic response indicators of train, buildings on the bridge and bridge of the structure of combination of bridge and buildings at different test speeds. The indicator of the 3 A vehicle running stability is calculated according to the equation w 7.08 F( f), where w is the f stability indicator, A is the vibration acceleration, f is the vibration frequency and F ( f ) is the frequency modified coefficient. When the vertical vibration frequency is 0.5~5.9Hz, F( f ) 0.35 f. According to The Dynamic Performance Evaluation and Test Evaluation Standard GB of Railway Vehicle, the criteria for the rank of vehicle running stability are: w.5, excellent;.5 w.75, good. We can get the security indicator of the bridge with reference to the requirements of UIC standard for the vibration acceleration of bridge in the design of bridge. The maximum vertical acceleration of the bridge on ballastless rail is limited as a max 0.50g. The vibration criteria of the buildings on the bridge considering people s comfortableness are calculated according to the vibration level ' VL 0log( a / a ) stipulated in ISO63-:997. In the equation, a 0 is reference acceleration rms 6 and is set as0 m/ s, a 0 ' rms is effective value of modified vibration acceleration. The limits can be referred to the stipulations about the generalized environment vibration in The Criteria for Environment Vibration in City Areas (GB ): the vertical z vibration level of the two sides of trunk railway is VL 80 (as the environment vibration value limit of the integrated bridge and z 5

8 building structure is not given, analysis is carried out with reference to the two sides of the trunk railway). Table. Model results V(km/h) w z UY(mm) UY (mm) VLz Conclusions This paper establishes the dynamic interactive model of the integral system of high-speed train, rail, bridge, buildings on the bridge and pier. Different from conventional vehicle-bridge model, this model considers the vibration of the rail structure and the effects of vehicle speed on running security and comfortableness while analyzing the dynamic response of the buildings on the bridge and people s comfortableness. It is calculated that the vertical z vibration level VL of the buildings on the bridge considering z people s comfortableness is 84.96, slightly higher than the vertical z vibration level of the two sides of the trunk railway referenced by literature [9-0]: VL 80. It can be derived from the analysis data z that vehicle speed has a small impact on the vertical displacement of the bridge mid-span and buildings on the bridge, and the stability is excellent. 5. References [] Chu K H,Garg V K, "Railway-bridge impact: simplified train and bridge mode ",Journal of the Struetural Division,ASCE,05,No.ST9,979 [] M H Bhatti, "Vertical and lateral dynamic response of railway bridges due to nonlinear vehicle and track irregularities ", Illinois Institute of Technology,Chicago,Illinois,98. [3] Diana G,Cheli F, "Dynamic Interaction of Railway Systems with Large Bridges ", Vehicle System Dynamics,Vol.8,No. -3,pp.7-06,989 [4] Xiaozhen Li, Wenbin Ma, Shizhong Qiang, "Numerical Solution to the Coupling Vibration Analysis of Vehicle-bridge System ", Vibration and Impact, No.3,00 [5] Xiaozhen Li, Shizhong Qiang, Ruili Shen, "Study on the Space Coupling Vibration Response of High-speed train long-span Steel Cable-stayed Bridge ", Bridge Construction,No. 4,998 [6] Yuping Wen, Ri Gao, Zhimin Liu, "Structural Study on Elevated Station of City Rail",Railway Construction, No. 3,000 [7] Wanming Zhai, "Vehicle-Rail Coupling Dynamics", nd version. Beijing: China Railway Publishing House, 00. [8] Jing Ji, Wenfu Zhang, Wenyan Zhao, Chaoqing Yuan, Yingchun Liu, "Research of Seismic Testing and Dynamic Character of High-rise Building Structure Based on ANSYS", JDCTA: International Journal of Digital Content Technology and its Applications, Vol. 6, No. 8, pp. 63-7, 0 [9] Xiaowei CHEN, "Application of Improved Genetic Algorithm in Optimum Design of Building Structures", AISS: Advances in Information Sciences and Service Sciences, Vol. 4, No. 3, pp , 0 [0] OUYANG Chengxin, XI Xiaoshuang, "Seismic Evaluation of Building with Additional Factor", JCIT: Journal of Convergence Information Technology,Vol. 6, No. 9, pp , 0 6