Numerical analysis of vehicle-bridge coupling vibration concerning nonlinear stress-dependent damping
Pengfei LI1,2, Jinquan ZHANG1,2(), Shengqi MEI2,3,4, Zhenhua DONG1,2, Yan MAO1,2
1. Bridge and Tunnel Technology Research Center, Research Institute of Highway, Ministry of Transport, Beijing 100088, China 2. National Engineering Laboratory of Bridge Structure Safety Technology, Research Institute of Highway, Ministry of Transport, Beijing 100088, China 3. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043, China 4. School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
Damping is known to have a considerable influence on the dynamic behavior of bridges. The fixed damping ratios recommended in design codes do not necessarily represent the complicated damping characteristics of bridge structures. This study investigated the application of stress-dependent damping associated with vehicle-bridge coupling vibration and based on that investigation proposed the stress-dependent damping ratio. The results of the investigation show that the stress-dependent damping ratio is significantly different from the constant damping ratio (5%) defined in the standard specification. When vehicles travel at speeds of 30, 60, and 90, the damping ratios of the bridge model are 3.656%, 3.658%, and 3.671%, respectively. The peak accelerations using the regular damping ratio are 18.9%, 21.3%, and 14.5% of the stress-dependent damping ratio, respectively. When the vehicle load on the bridge is doubled, the peak acceleration of the mid-span node increases by 5.4 times, and the stress-related damping ratio increases by 2.1%. A corrugated steel-web bridge is being used as a case study, and the vibration response of the bridge is compared with the measured results. The acceleration response of the bridge which was calculated using the stress-dependent damping ratio is significantly closer to the measured acceleration response than that using the regular damping ratio.
P Paultre, O Chaallal, J Proulx. Bridge dynamics and dynamic amplification factors—A review of analytical and experimental findings. Canadian Journal of Civil Engineering, 1992, 19( 2): 260– 278 https://doi.org/10.1139/l92-032
2
E Khan, J A Lobo, D G Linzell. Live load distribution and dynamic amplification on a curved prestressed concrete transit rail bridge. Journal of Bridge Engineering, 2018, 23( 6): 04018029 https://doi.org/10.1061/(ASCE)BE.1943-5592.0001236
3
C Broquet, S F Bailey, M Fafard, E Brühwiler. Dynamic behavior of deck slabs of concrete road bridges. Journal of Bridge Engineering, 2004, 9( 2): 137– 146 https://doi.org/10.1061/(ASCE)1084-0702(2004)9:2(137
4
L Deng, Y Yu, Q Zou, C S Cai. State-of-the-art review of dynamic impact factors of highway bridges. Journal of Bridge Engineering, 2015, 20( 5): 04014080 https://doi.org/10.1061/(ASCE)BE.1943-5592.0000672
5
Y B Yang, Z L Wang, K Shi, H Xu, J P Yang. Adaptive amplifier for a test vehicle moving over bridges: Theoretical study. International Journal of Structural Stability and Dynamics, 2021, 21( 3): 2150042 https://doi.org/10.1142/S0219455421500425
6
S E Abdel Raheem. Dynamic characteristics of hybrid tower of cable-stayed bridges. Steel and Composite Structures, 2014, 17( 6): 803– 824 https://doi.org/10.12989/scs.2014.17.6.803
7
J Mashhadi, H Saffari. Effects of damping ratio on dynamic increase factor in progressive collapse. Steel and Composite Structures, 2016, 22( 3): 677– 690 https://doi.org/10.12989/scs.2016.22.3.677
8
H D Zhang, J Wang, X Zhang, G Liu. Effects of viscous damping models on a single-layer latticed dome during earthquakes. Structural Engineering and Mechanics, 2017, 62( 4): 455– 464 https://doi.org/10.12989/sem.2017.62.4.455
9
Y Fujino, K Kimura, H Tanaka. Wind Resistant Design of Bridges in Japan: Developments and Practices. Berlin: Springer Science & Business Media, 2012
10
R M Barker, J A Puckett. Design of Highway Bridges: An LRFD Approach. New Jersey: John Wiley & Sons, 2013
11
A Alipour, B Shafei, M Shinozuka. Performance evaluation of deteriorating highway bridges located in high seismic areas. Journal of Bridge Engineering, 2011, 16( 5): 597– 611 https://doi.org/10.1061/(ASCE)BE.1943-5592.0000197
12
P Code. Eurocode 8: Design of Structures for Earthquake Resistance. Brussels: European Committee for Standardization, 2001
13
S D C Caltrans. Caltrans Seismic Design Criteria. Version 1.6. Sacramento, CA: California Department of Transportation, 2010
14
R Green. Dynamic response of bridge superstructures-Ontario observations. In: Proceeding of a Symposium of Dynamic Behavior of Bridges at the Transport and Road Research Laboratory. Crowthorne: Transport and Road Research Laboratory (TRRL), 1977
15
J R Billing. Dynamic loading and testing of bridges in Ontario. Canadian Journal of Civil Engineering, 1984, 11( 4): 833– 843 https://doi.org/10.1139/l84-101
J R Casas. Full-scale dynamic testing of the Alamillo cable-stayed bridge in Sevilla (Spain). Earthquake Engineering & Structural Dynamics, 1995, 24( 1): 35– 51 https://doi.org/10.1002/eqe.4290240104
18
F Myrvoll, A M Kaynia, E Hjorth-Hansen, E Strømmen. Full-scale dynamic performance testing of the bridge structure and the special cable friction dampers on the cable-stayed Uddevalla bridge. In: Proceeding of 20th IMAC Conference on Structural Dynamics, Los Angeles: SPIE Press, 2002
19
F Magalhães, Á Cunha, E Caetano, R Brincker. Damping estimation using free decays and ambient vibration tests. Mechanical Systems and Signal Processing, 2010, 24( 5): 1274– 1290 https://doi.org/10.1016/j.ymssp.2009.02.011
20
C Rebelo, da Silva L Simões, C Rigueiro, M Pircher. Dynamic behavior of twin single-span ballasted railway viaducts—Field measurements and modal identification. Engineering Structures, 2008, 30( 9): 2460– 2469 https://doi.org/10.1016/j.engstruct.2008.01.023
21
M Ülker-Kaustell, R Karoumi. Application of the continuous wavelet transform on the free vibrations of a steel–concrete composite railway bridge. Engineering Structures, 2011, 33( 3): 911– 919 https://doi.org/10.1016/j.engstruct.2010.12.012
22
M Ülker-Kaustell, R Karoumi. Influence of nonlinear stiffness and damping on the train-bridge resonance of a simply supported railway bridge. Engineering Structures, 2012, 41 : 350– 355 https://doi.org/10.1016/j.engstruct.2012.03.060
23
G C Hart, R Vasudevan. Earthquake design of buildings: Damping. Journal of the Structural Division, 1975, 101( 1): 11– 30 https://doi.org/10.1061/JSDEAG.0003964
R Eyre, G P Tilly. Damping measurements on steel and composite bridges. In: Proceeding of a Symposium on Dynamic Behavior of Bridges at the Transport and Road Research Laboratory. Crowthorne: Transport and Road Research Laboratory (TRRL), 1977
26
G P Tilly. Damping of highway bridges: A review. In: Proceeding of a Symposium on Dynamic Behavior of Bridges at the Transport and Road Research Laboratory. Crowthorne: Transport and Road Research Laboratory (TRRL), 1977
27
M F Green, D Cebon. Modal testing of two highway bridges. In: Proceeding of 11th International Modal Analysis Conference. Kissimme (FL): Society for Experimental Mechanics, 1993
28
J L Hou, W B Xu, Y J Chen, K Zhang, H Sun, Y Li. Typical diseases of a long-span concrete-filled steel tubular arch bridge and their effects on vehicle-induced dynamic response. Frontiers of Structural and Civil Engineering, 2020, 14( 4): 867– 887 https://doi.org/10.1007/s11709-020-0649-9
29
Z Sun. Moving-inertial-loads-induced dynamic instability for slender beams considering parametric resonances. Journal of Vibration and Acoustics, 2016, 138( 1): 011014 https://doi.org/10.1115/1.4031518
30
Z Jin, B Huang, S Pei, Y Zhang. Energy-based additional damping on bridges to account for vehicle-bridge interaction. Engineering Structures, 2021, 229 : 111637 https://doi.org/10.1016/j.engstruct.2020.111637
31
B Glatz, J Fink. A redesigned approach to the additional damping method in the dynamic analysis of simply supported railway bridges. Engineering Structures, 2021, 241 : 112415 https://doi.org/10.1016/j.engstruct.2021.112415
32
C D Stoura, E G Dimitrakopoulos. Additional damping effect on bridges because of vehicle-bridge interaction. Journal of Sound and Vibration, 2020, 476 : 115294 https://doi.org/10.1016/j.jsv.2020.115294
33
B J Lazan. Damping of Materials and Members in Structural Mechanics. Oxford: Pergamon Press, 1968
34
Y F Wang, Y H Pan, J Wen, L Su. Material damping evaluation of frames made of different materials. Materials Research Innovations, 2014, 18( sup3): 53– 58
G D Gounaris, N K Anifantis. Structural damping determination by finite element approach. Computers & Structures, 1999, 73( 1-5): 445– 452 https://doi.org/10.1016/S0045-7949(98)00257-0
37
G D Gounaris, E Antonakakis, C A Papadopoulos. Hysteretic damping of structures vibrating at resonance: An iterative complex eigensolution method based on damping-stress relation. Computers & Structures, 2007, 85( 23−24): 1858– 1868 https://doi.org/10.1016/j.compstruc.2007.02.026
38
S Q Mei, L Su, P F Li, Y Wang. Material damping of concrete under cyclic axial compression. Journal of Materials in Civil Engineering, 2018, 30( 3): 04017295 https://doi.org/10.1061/(ASCE)MT.1943-5533.0002146
39
L Su, Y F Wang, P F Li, S Mei, K Guo. Seismic analysis of bridges based on stress-dependent damping. Structural Engineering and Mechanics, 2017, 62( 3): 281– 289 https://doi.org/10.12989/sem.2017.62.3.281