21 ANSYS Yang NEWMARK v c z φ c c v t φ t t v w w APDL AN- k y1 k y2 c y1 c y2 SYS - l l c l t - Lagrange

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1 32 21 JOURNAL OF VIBRATION AND SHOCK Vol. 32 No ANSYS BAG12A1 - K ANSYS - UPF ANSYS UPF U A Seimic repone analyi of a time-varying high peed train -rail-bridge ytem baed on ANSYS LIU Chang-liang YIN Xun-qiang LIN Gao LI Jian-bo HU Zhi-qiang Laboratory of Earthquake State Key Laboratory of Coatal and Offhore Engineering Dalian Univerity of Technology Dalian China Abtract Uing ANSYS oftware platform a time-variant wheel-rail coupled element with artificial node wa introduced combining application of uer programmable feature UPF a dynamic FE model for the eimic repone analyi of a high-peed vehicle-rail-bridge ytem wa formed and embedded in the popular finite element oftware ANSYS. With the propoed approach the dynamic interaction of rail and bridge wa modeled with ma-pring-dahpot ytem the vehicle ubytem wa modeled a a rigid-body dynamic model. The vehicle-rail-bridge ytem wa aembled through atifying the geometric compatibility and balance of the interaction force on the connected node. Earthquake acceleration time hitorie a the input excitation to the ytem were applied to the rail-bridge ubytem with the largema method. Finally the reliability and good erviceability of the propoed time-varying ytem were verified through numerical example and it application to actual engineering project. It wa hown that thi time-varying ytem model ha the potential to olve ophiticated and real engineering problem combined with the rich element library and nonlinear olver available in the commercial finite element oftware ANSYS. Key word high-peed train time-varying ytem eimic repone analyi ANSYS UPF

2 21 ANSYS Yang NEWMARK v c z φ c c v t φ t t v w w APDL AN- k y1 k y2 c y1 c y2 SYS - l l c l t - Lagrange ANSYS UPF M uu M uw uu M wu M C uu C uw uu ww u C w wu C ww uw K uu K uw u K wu K u F ww u = u w F T u w T R 1 w u w M C K 1 - u F - R - T T u = Newmark x y z 2 Fig. 2 Sketch of train ubytem model Fig. 1 Sketch map of high peed train-tail-bridge time-variant ytem ubjected to eimic excitation 3 - Fig. 3 Sketch of rail-bridge ubytem model

3 R = T -1 w M ww u * w C ww u * w K ww u * w M wu u u C wu u u K wu u u - F w 5 u * w =? Г?N v? 1 u r1 r x 1 Г?N v? i u ri r x i? T * uw Bemoulli-Euler * uw 3-5 k bx k by c bx - c by M * r ur C M r ur M b M C r C - C M u b M * r - C ur L u - C r L u - C T b C b C T b C b C ub u K * r - K u b K r K - K u - K T K b r F K u r - R - K = b F 2 b M u L T K b r F K u r R = b F * 6 b M L u g g M r b * r = M r - - δ nw N v i T -1 w M wwij Γ?N v? j 7a w = 1 R C * r = C u g M L r C δ nw N v i T -1 w C wwij Γ?N v? j 7b w = K * r = K r K Hermitian δ nw N v i T -1 w K wwij Γ?N v? j 7c C = ne c bx l N u?n u?dx c by l w = 1 N v?n v?dx 3a R * r = - N v i T -1 w K wwi r x i el = 1 K = ne k bx l N u?n u?dx k by el = 1 l M wui u ui C wu u ui K wui u ui F wi 7d N v?n v?dx 3b δ δ = 1 N u N v δ = nw l ne M L M b i u wi = Г?N v? i u ri r x i 4 Г Newmark r x u ri -

4 21 ANSYS ANSYS ANSYS Fig. 5 Activated of time-variant wheel-rail coupling element - - ANSYS - ANSYS Rayleigh α β b c * r = δ N v t -1 w c ww - αm ww - βk ww Γ?N v? 9-4 ANSYS ANSYS i j i 1 1 j ANSYS Fig. 4 Time-variant wheel-rail - coupling element with virtual node UerElem. f 2 k k * - k = 5 - k T k B c c 7c * - c k = - c T c - k - β - k T k 1 k c k * r = k r δ N v ξ c t -1 w k ww Γ?N v ξ c? k r δ = 1-7 a - 7 b A C δ = ANSYS ANSYS ANSYS UerElem. f 13 ANSYS UPF FORTRAN

5 Newmark 6 L = 25 m I = 2. 9 m 4 E = 2. 87E9 Pa m = 2 33 kg /m ν =. 2 - M v = 5 75 kg k v = kn /m 2. 4 ANSYS 1-5 kg I t = 1 kg m 4 M w = 1-5 kg k y1 = 1 1 kn /m ANSYS - k y2 =. 5 k v = kn /m c y1 = c y2 = kn /m - l c = l t = l = m E r = 21 GPa v r =. 3 I r = 1-1 m 4 m r = 1-1 kg /m k by = 1 1 kn /m 2 c by = kn / m 2 E b = E = GPa v b = v =. 3 I b = I = 2. 9 m 4 m b = m = 233 kg /m ANSYS APDL 1 BEAM3 ANSYS ANSYS - - Tab. 1 Flowchart of the etablihment of propoed model 1. - APDL 2. Uer1. f Uer2. f APDL 2 - UerElem. f Fig. 7 The midpoint diplacement of the beam ANSYS 4 1 Uer2. f 4. APDL 3 v = m / M c = M v = 5 75 kg = 1 kg m 4 M t = 7 6 I c - 8 Fig. 6 A imple beam ubjected to a moving pring-ma train model Fig. 8 The acceleration repone of the prung ma

6 21 ANSYS mm mm. 159 mm. 16 mm mm mm 3 15 ANSYS mm mm m m / m / 2 m 5. 5 m 2. 3 m. 52 m / m / 2 15 beam3. 17 m / m / 2 ma m / m / 2 CP - - ma21 - Rayleigh El Centro 8 gal 9 9 El Centro Fig. 9 Acceleration time domain of El Centro earthquake 1 Fig. 1 The vertical diplacement repone at the midpoint of 3rd bridge with and without eimic extraction km /h 11 3 Fig. 11 The vertical diplacement repone at the midpoint 11 of 3rd rail with and without eimic extraction

7 moving load and upport motion due to earthquake J. Journal of Sound and Vibration /2 218 Fig. 12 The vertical acceleration repone of the 1t and 15th vehicle of train on bridge with and without eimic extraction J TAN Chang-jian ZHU Bing. Coupled vibration analyi of high peed train and bridge ubjected to eimic excitation - J. Journal of Vibration and Shock De Roeck Guido J ANSYS ZHANG Nan XIA He. Analyi of a vehicle-bridgeearthquake interactive ytem under multi-upport excitation J. Journal of Harbin Engineering Univerity ANSYS ANSYS J WANG Shao-lin ZHAI Wan-ming. Dynamic repone of high-peed train-track-bridge ytem under eimic excitation J. Journal of Southwet Jiaotong Univerity Yang Y B Y. Wu S. Dynamic tability of train moving over bridge haken by earthquake J. Journal of Sound and Vibration ANSYS D ANSYS J YANG Jian-rong LI Jian-zhong FAN Li-chu. Analyi on vehicle-bridge coupling vibration baed on ANSYS J. 1. Computer Aided Engineering J Yang Y B Yau J D Wu Y S. Vehicle-bridge interaction ZHANG Nan XIA He. Influence of earthquake on running dynamic M. Singapore World cientific publihing 24. afety of vehicle on multi-pan girder bridge J. Word 12 Leger P Ide I M Paultre P. Multiple upport eimic Information on Earthquake Engineering analyi of large tructure J. Computer and Structure ANSYS Incorporated. Programmer' Manual for ANSYS J M Bigg J M. Introduction to tructural dynamic M. HAN Yan XIA He GUO Wei-wei. Dynamic Repone of McGraw-Hill New York cable-tayed bridge to running train and earthquake J. 15 Wu Y S. Dynamic interaction of train-rail-bridge ytem Engineering Mechanic J XIONG Jian-zhen GAO Mang-mang YU Han-bin. Vehiclebridge coupling vibration analyi of cable-tayed bridge of tianxingzhou yangtze river bridge under earthquake J. China Railway Science Ladilav F B Yau J D. Supended bridge ubjected to under normal and eimic condition D. Taiwan National Taiwan Univerity 2.