Abstract
The dynamic finite element equation of the vehicle-track nonlinear coupling system is a large, high-order and nonlinear coupled second-order differential equation set, the efficiency of the conventional algorithm for solving the large and complicated differential equation set is not satisfied. In this chapter, the cross-iterative algorithm for solving the dynamic finite element equation of nonlinear vehicle-track coupling system is described, and the algorithm verification and convergence analysis is carried out by given examples. In simulation analysis, the whole system is divided into two subsystems, i.e., the vehicle subsystem considered as a rolling stock unit with a primary and secondary suspension system, and the track or the track-bridge subsystem regarded as a three elastic beam model. Coupling of the two systems is achieved by equilibrium conditions for wheel-rail nonlinear contact forces and geometrical compatibility conditions. In order to accelerate the iterative convergence, a relaxation technique is introduced to modify the wheel-rail contact forces. The cross-iteration algorithm has the shining advantages of higher efficiency, better precision and simple programming. Based on the proposed model and the algorithm, the source program “Train-track-continuous bridge coupling system dynamics calculation progam VTBDYN_1.0” is developed by MATLAB mathematical tools, and given in Appendix C.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Clough RW, Penzien J (1995) Dynamic of structures (3rd Edition). Computers & Structures, Inc., Berkeley, pp 120–124
Rezaiee-Pajand M, Alamatian J (2008) Numerical time integration for dynamic analysis using a new higher order predictor-corrector method. Eng Comput 25(6):541–568
Chen C, Ricles JM (2010) Stability analysis of direct integration algorithms applied to MDOF nonlinear structural dynamics. J Eng Mech 136(4):485–495
Zhai WM (2007) Vehicle-track coupling dynamics (3rd edition). Science Press, Beijing
Nan Z, He X (2013) A vehicle-bridge interaction dynamic system analysis method based on inter-system iteration. China Railway Sci 34(5):32–38
Dingjun Wu, Qi Li, Airong C (2007) Numerical stability of iterative scheme in solving coupled vibration of the train-bridge system. Chin Q Mech 28(3):405–411
Yang F, Fonder GA (1996) An iterative solution method for dynamic response of bridge-vehicles systems. J Earthq Eng Struct Dyn 25(2):195–215
Bin Z, Xiaoyan L (2011) Analysis on dynamic behavior of ballastless track based on vehicle and rack elements with finite element method. J China Railway Soc 33(7):78–85
Jun X, Danm H, Qingyunan Z (2007) Analysis method of vertical vibration of train and ballastless track system with the lateral finite strip and slab segment element. J China Railway Soc 29(4):64–69
Xiayan L (2002) New methods in railroad track mechanics & technology. China Railway Publishing House, Beijing
Lei X, Zhang B, Liu Q (2010) A track model for vertical vibration analysis of track-bridge coupling. J Vibr Shock 29(3):168–173
Xiaoyan L (2000) Finite element method. China Railway Publishing House, Beijing
Zhang B, Lei X, Luo Y (2016) Improved algorithm of iterative process for vehicle-track coupled system based on Newmark formulation. J Central South Univ (Sci Technol) 47(1):298–306
Lei X, Wu S, Zhang B (2016) Dynamic analysis of the high speed train and slab track nonlinear coupling system with the cross iteration algorithm. J Nonlinear Dyn, vol 2016, Article ID 8356160, 17 pages, shttps://doi.org/10.1155/2016/8356160 .
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 Science Press
About this chapter
Cite this chapter
Lei, X. (2022). A Cross-Iteration Algorithm for Vehicle–Track Nonlinear Coupling Vibration Analysis. In: High Speed Railway Track Dynamics. Advances in High-speed Rail Technology. Springer, Singapore. https://doi.org/10.1007/978-981-16-4593-8_7
Download citation
DOI: https://doi.org/10.1007/978-981-16-4593-8_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-4592-1
Online ISBN: 978-981-16-4593-8
eBook Packages: EngineeringEngineering (R0)