32 1 Vol 32 1 2011 1 Journal of Harbin Engineering University Jan 2011 doi 10 3969 /j issn 1006-7043 2011 01 006 - - 1 2 1 De Roeck Guido 2 1 100044 2 B - 3001 Kalker - U448 A 1006-7043 2011 01-0026-07 Analysis of a vehicle-bridge-earthquake interactive system under multi-support excitations ZHANG Nan 1 2 XIA He 1 DE ROECK Guido 2 1 School of Civil Engineering Beijing Jiaotong University Beijing 100044 China 2 Department of Civil Engineering Catholic U- niversity of Leuven Belgium B-3001 Abstract When a high-speed train crosses a long-span bridge the safety of the train is obviously affected by the occurrence of an earthquake In order to study the dynamic characteristics of a coupled vehicle-bridge system under seismic loads the vehicle subsystem was modeled by the rigid-body dynamics method and the bridge subsystem was modeled by the finite element method The vertical and lateral wheel-rail interactive forces were defined by the corresponding wheel-rail interactive assumption and simplified Kalker creep theory the track irregularities and calculated seismic acceleration histories were regarded as the system exciter The seismic effects were imposed as multisupported excitations to the bridge subsystem by the large-mass method the motion equations were solved by the history integral method and force-motion iterations within time steps The results show that the bridge vibration derailment factors and offloading factors of the vehicle increase markedly with the seismic intensity there is no monotonous variation relationship between vehicle-bridge response and the seismic wave velocity Keywords vehicle-bridge interacted system seismic load multi-supported excitation large-mass method railway cable-stayed bridge train speed threshold 2009-09-22 90715008 - BIL07 /07 1971-1951- hxia88@ 163 com 1-5
1 - - 27 c X2 c Y2 c Z2 X Y Z b 1 b 2 d 1 d 1 2 h 1 - - h 2 - - h 3 Y Z RX RY RZ 6 Y RZ Lagrange - - - 6 - - - X Z Y RX RY RZ X Y Z 1 1 M V X V + C V X V + K V X V = F V 1 23 M V C V K V 1 F V Fig 1 Vehicle element model 1 2 1-5 M B + M L X B + M V BX B + K B X B = M V1 0 F M B + M L A G 3 V2 M V = 2 M B C B K B F B 0 M Vn M L M Vn n A G M L A G 0 1 2 4 m D 1 M V = 4 k X1 k Y1 k Z1 m X Y Z c X1 c Y1 c Z1 D 0 X Y Z k X2 k Y2 k Z2 A G = a G N1 a G N2 T 5 X Y Z m D M B
28 32 10 3 ~ 10 5 N 1 N 2 Z 1 2 = Z J - sr YJ b 1 R XJ a G Ni N i Z 3 4 = Z D + Z I b 1 R XI 4 5M L N 1 N 2 Z m 0 0 A G N 1 N 2 I = Z IL + Z IR 8 2 0 R XI = R XD + Z IR - Z IL M L A g 0 G g 0 s = d 1 s = - d 1 Z J 3M B C B K B R XJ R YJ Z RX RY Z D R XD N 1 N 2 Z RX Z IL Z IR M B C B K B Z F 1 F 2 M L F 1 = k Z1 Z 1 - Z 3 + c Z1 Z 1 - Z 3 9 M B C B K B { F 2 = k Z1 Z 2 - Z 4 + c Z1 Z 4 I X0 + R XI + b 1 F 1 - F 2 10 g 0 m 0 I X0 RX Z ΔE ΔE E = lim = lim Δt ΔX /V = E V lim = lim V lim ΔE Δt ΔE ΔX = V E X = lim ΔE ΔX /V = ΔE ΔX = V2 2 E X 2 6 7 E V 1 4 2 - Z 4 Z 1 Z 2 Z 3 Z 4 2 1 2 3 4 1 3 F 3 F 4 F 3 4 = m 0Z I + F 1 + F 2 2 F 3 F 4 G a - b - 2 Fig 2 Wheel-rail vertical interacted forces 1 5 2 F 1 F 2 Z F 3 F 4 3 Z G 2 1 2 3 4 X RZ
1 - - 29 Y 10 Kalker Y RZ F 5 6 = f 11g 0 R ZW 2V F 7 8 = - f 22 Y W - Y D - Y IL IR 11 V R ZW F 9 = F 10 = - V f 11 f 22 f 33 7 8 Y W R ZW Y RZ Y D Y Y IL Y IR Y 120 + 5 168 + 120 m 3 Fig 3 Wheel-rail lateral interacted forces 100 63 2% 1 6-1 3-2 1 M V X V + C V X V + K V X V = V V 120 + 5 168 + 120 m { M B + M L X B + C B X B + K B X B = F B + M L A G 6 12 5 2 A G 32 5 m 12 7 m MIDAS Civil Newmark- 9 12 F V F B m Rayleigh 8 ~ 11 0 01 8 ~ 11-5 6 4 5 1 Fig 4 4 2 Iteration process within time step ICE3
30 32 b 5 Fig 5 Standard cross-section of bridge deck 6 Fig 6 Bridge finite element method model c 1 Table 1 Frequencies and modes of the bridge f /Hz 1 0 587 2 0 651 3 0 687 4 0 755 5 0 850 2 2 ICE3 16 24 775 m 160 kn 11 146 kn 4 3 1 100 100 63 2% 150 ~ 450 km /h 25 km /h 12 2 3 41 5 gal 27 7 gal 8 10 1 ~ 80 m 11 80 mm 10 79 3 5 000 3 000 1 000 m 7 Fig 7 7 d Track irregularity 2 4 1 000 m /s a a
1 - - 31 Fig 8 8 b Seismic acceleration history 2 5 1 d 9 - - Fig 9 Vehicle-bridge system response history Q /P P /P Q P P c a 3 000 m /s 350 km /h 1 1 9 b 10 c a b d 10 Fig 10 Vehicle-bridge response vs train speed
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