Effective Mode Shapes of Viaducts Subjected to High-speed Train

Year 2021, , 295 - 307, 15.01.2021

Salih Demirtaş , Hasan Öztürk

https://doi.org/10.21205/deufmd.2021236726

Abstract

The high-speed railways require more viaducts than conventional railways. The dynamic interaction effect between train and viaduct are important issue due to the risk of derailment, structural safety and deterioration of the passenger comfort. In this study, viaduct is modelled as a multi-bay frame. The multi-bay frame is modelled by finite element method. The train is idealized as a two-axle system with 4 degrees of freedom. The equations of motions of the coupled vehicle-structure system are determined via generalized Lagrange's equation. The Wilson-theta time integration method is employed to determine the dynamic response of the system. The effective mode shapes are investigated using 3D frequency-velocity-amplitude graphs. The resonant response has been determined at first and second modes of 1 and 2-bay frames.

Keywords

viaduct, mode shape, , finite element method, Wilson-theta method, train

Supporting Institution

-

Project Number

-

Thanks

-

Hızlı Tren Geçişine Maruz Kalan Viyadüklerin Etkin Mod Şekilleri

Abstract

Yüksek hızlı demiryolları, geleneksel demiryollarından daha fazla viyadük gerektirir. Tren ve viyadük arasındaki dinamik etkileşim etkisi, raydan çıkma, yapısal güvenlik ve yolcu konforunun bozulması nedeniyle önemli bir konudur. Bu çalışmada viyadük çok bölmeli bir çerçeve olarak düşünülmüştür. Çok bölmeli çerçeve sonlu elemanlar yöntemi ile modellenmiştir. Tren, 4 serbestlik dereceli iki akslı sistem olarak idealize edilmiştir. Birleştirilmiş araç-yapı sisteminin hareket denklemleri genelleştirilmiş Lagrange denklemi ile belirlenmiştir. Sistemin dinamik yanıtını belirlemek için Wilson-teta zaman integrasyonu yöntemi kullanılmıştır. Etkin mod şekilleri, 3D frekans-hız-genlik grafikleri kullanılarak araştırılmıştır. 1 ve 2 bölmeli çerçevelerin birinci ve ikinci modlarının, yapının rezonans cevabında baskın olduğu belirlenmiştir.

Keywords

viyadük, mod şekli, sonlu elemanlar metodu, Wilson-theta metodu, tren

Project Number

-

References

• Su, D., Fujino, Y., Nagayama, T., Hernandez, J. Y., Seki, M. 2010. Vibration of reinforced concrete viaducts under high-speed train passage: Measurement and prediction including train-viaduct interaction, Structures and Infrastructures Engineering, vol. 6, no. 5, pp. 621–633, 2010, DOI: 10.1080/15732470903068888.
• Lou, P., Dai, G. L., Zeng Q. Y. 2005. Modal coordinate formulation for a simply supported bridge subjected to a moving train modelled as two-stage suspension vehicles, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 219, no. 10, pp. 1027–1040. DOI: 10.1243/095440605X31940.
• Duan, Y. F., Wang, S. M., Wang, R. Z., Wang, C. Y., Shih, J. Y., Yun, C. B., 2018. Vector Form Intrinsic Finite-Element Analysis for Train and Bridge Dynamic Interaction, Journal of Bridge Engineering, vol. 23, no. 1, pp. 1–15. DOI: 10.1061/(ASCE)BE.1943-5592.0001171.
• Hubbell, D., Gauvreau, P. 2018. Frequency Domain Analysis of Train – Guideway Interaction Dynamics, Journal of Structural Engineering, vol. 144, no. 8, pp. 1–11. DOI: 10.1055/s-0035-1570321.
• Wu, Y. S., Yang, Y.-B. 2003. Steady-state response and riding comfort of trains moving over a series of simply supported bridges, Engineering Structures, vol. 25, no. 2, pp. 251–265. DOI: 10.1016/S0141-0296(02)00147-5.
• Youcef, K., Sabiha, El Mostafa, T., D., Ali, D., Bachir, M. 2013. Dynamic analysis of train-bridge system and riding comfort of trains with rail irregularities, Journal of Mechanical Science and Technology, vol. 27, no. 4, pp. 951–962, DOI: 10.1007/s12206-013-0206-8.
• Biondi, B., Muscolino, G., Sofi, A. 2005. A substructure approach for the dynamic analysis of train-track-bridge system, Computers and Structures, vol. 83, no. 28-30 SPEC. ISS., pp. 2271–2281. DOI: 10.1016/j.compstruc.2005.03.036.
• Xiang, T., Zhao, R., Xu, T. 2007. Reliability Evaluation of Vehicle–Bridge Dynamic Interaction, Journal of Structural Engineering, vol. 133, no. 8, pp. 1092–1099, 2007. DOI: 10.1061/(ASCE)0733-9445(2007)133:8(1092).
• Yang, Y.-B., Yau, J.-D., Hsu, L.-C. 1997. Vibration of simple beams due to trains moving at high speeds, Engineering Structures, vol. 19, no. 11, pp. 936–944. DOI: http://dx.doi.org/10.1016/S0141-0296(97)00001-1.
• Lin, C. C., Wang, J. F., Chen, B. L. 2005. Train-Induced Vibration Control of High-Speed Railway Bridges Equipped with Multiple Tuned Mass Dampers, Journal of Bridge Engineering, vol. 10, no. 4, pp. 398–414. DOI: 10.1061/(ASCE)1084-0702(2005)10:4(398).
• Demirtas, S., Ozturk, H., Sabuncu, M. 2019. Dynamic Response of Multi-bay Frames Subjected to Successive Moving Forces,” International Journal of Structural Stability and Dynamics, vol. 19, no. 4, pp. 1–24, DOI: 10.1142/S0219455419500421.
• Bathe, K.-J. 1996 Finite Element Procedures. Prentice Hall, Upper Saddle River, New Jersey.
• Yang, Y.-B., Chang, C., Yau, J. 1999. An Element for Analysing Vehicle Bridge Systems Considering Vehicle’s Pitching Effect, International Journal for Numerical Methods in Engineering, no. 46, pp. 1031–1047.