Balastlı Demiryolu Hatlarının Statik Analizinde Diferansiyel Dönüşüm Yönteminin Uygulanması

Yıl 2023, Cilt: 9 Sayı: 2, 528 - 539, 31.12.2023

İlker Şahinoğlu , Kanat Burak Bozdoğan

https://doi.org/10.34186/klujes.1397981

Öz

Mühendislikte birçok problem belirli kabuller altında basitleştirilmekte ve basitleştirilmiş modelin matematik modeli kurularak analitik ya da sayısal yöntemler ile çözüme ulaşılmaktadır. Bu basitleştirilmiş modellerden birisi de elastik zemine oturan kiriş teorisidir. Elastik zemine oturan kiriş teorisi demiryolu hatlarının çözümünde kullanılan ve uygun sonuçlar veren bir yaklaşımdır. Elastik zemine oturan kiriş problemlerinin modellenmesinde kullanılan en basit yaklaşım ise zeminin kirişe etkisini tek bir parametre ile temsil eden Winkler zemin modelidir. Bu çalışmada balastlı demiryolu hatlarının statik analizi için diferansiyel dönüşüm yöntemi yaklaşımı önerilmiştir. Çalışmada balastlı demiryolu hattı literatürden bilinen Winkler zeminine oturan bir Euler-Bernoulli kirişi olarak modellenmiştir. Önce eşdeğer Winkler zeminine oturan kirişin diferansiyel denklemi ve sınır koşulları yazılmış daha sonra çözümü kolaylaştırmak için diferansiyel denklem ve sınır koşulları boyutsuz hale getirilmiştir. Boyutsuz dördüncü mertebeden adi diferansiyel denklemin çözümü sınır koşulları dikkate alınarak diferansiyel dönüşüm yöntemi ile gerçekleştirilmiştir. Çalışmanın sonunda diferansiyel dönüşüm yöntemi ile çözümün uygunluğunu araştırmak üzere literatürden alınan bir örnek çözülmüş ve sonuçlar değerlendirilmiştir.

Anahtar Kelimeler

Balastlı demiryolu hattı, Winkler zemin modeli, Diferansiyel dönüşüm yöntemi, Statik analiz

Application of the Differential Transform Method in Static Analysis of Ballasted Railway Tracks

Öz

Many problems in engineering are simplified under certain assumptions and a mathematical model of the simplified model is created and the solution is reached using analytical or numerical methods. One of these simplified models is the theory of beams resting on elastic foundations. Beam theory resting on elastic foundation is an approach used in the solution of railway track and gives suitable results. The simplest approach used in modeling problems of beams resting on elastic foundations is the Winkler soil model, which represents the effect of the soil on the beam with a single parameter. In this study, the differential transformation method approach is proposed for the static analysis of ballasted railway track. In the study, the ballasted railway track was modeled as an Euler-Bernoulli beam resting on the Winkler foundation, known from the literature. First, the differential equation and boundary conditions of the beam resting on the equivalent Winkler foundation were written, and then the differential equation and boundary conditions were made dimensionless to facilitate the solution. The solution of the dimensionless fourth-order ordinary differential equation was carried out by the differential transformation method, considering the boundary conditions. At the end of the study, an example taken from the literature was solved to investigate the suitability of the solution with the differential transformation method and the results were evaluated.

Anahtar Kelimeler

Ballasted railway track, Winkler soil model, Differential transform method, Static analysis

Kaynakça

• Indraratna, B., Salim, W. and Rujikiatkamjorn, C. (2011). Advanced rail geotechnology - ballasted track (1st ed.). CRC Press. https://doi.org/10.1201/b10861
• Selig, E. T. and Waters, J. M., (1994). Track geotechnology and substructure management, Thomas Telford Publications, London, ISBN: 0 7277 2013 9.
• Guo, Y., Xie, J., Fan, Z., Markine, V., Connolly, D. P. and Jing, G. (2022). Railway ballast material selection and evaluation: A review. Construction and Building Materials, 344, 128218. https://doi.org/10.1016/j.conbuildmat.2022.128218
• Burrow, M. P. N., Bowness, D. and Ghataora, G. S. (2007). A comparison of railway track foundation design methods. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 221(1), 1-12. https://doi.org/10.1243/09544097JRRT58
• Kalliainen, A., Kolisoja, P. and Nurmikolu, A. (2016). 3D finite element model as a tool for analyzing the structural behavior of a railway track. Procedia engineering, 143, 820-827. https://doi.org/10.1016/j.proeng.2016.06.133
• Lassoued, R. and Guettiche, A., (2011). Mechanical behaviour of railway track, Physics Procedia, Volume 21, 2011, Pages 166-173, ISSN 1875-3892, https://doi.org/10.1016/j.phpro.2011.10.025
• Winkler, E. (1867). Die Lehre von der Elastizitätund Festigkeit, mit Besonderer Rücksicht auf ihre Anwendung in der Technik. H. Dominicus, Prague, Czech Republic.
• Sadeghi J. (1997). Investigation of characteristics and modeling of railway track system, PhD Thesis, Department of Civil Mining, and Environmental Engineering, the University of Wollongong, Australia.
• Cai, Z., Raymond, G. P. and Bathurst, R. J. (1994). Estimate of static track modulus using elastic foundation models. Transportation Research Record, 1470, 65.
• Zimmermann, H., (1888). Die Berechnung des Eisenbahnoberbaues (The analysis of the railroad track, In German), Verlag W. Ernst and Sohn, Berlin, 1888.
• Kerr, A. D. (1976). On the stress analysis of rails and ties (No. DOT-TSC-FRA-76-16). United States. Federal Railroad Administration.
• Hetényi, M. (1946). Beams on elastic foundation theory with applications ın the fields of civil and mechanical engineering. University of Michigan Press, Michigan, 255 s.
• Ahlbeck, D. R., Meacham, H. C. and Prause, R. H. (1978). The development of analytical models for railroad track dynamics. In Railroad track mechanics and technology (pp. 239-263). Pergamon. https://doi.org/10.1016/B978-0-08-021923-3.50017-6
• Suiker, A. S. and de Borst, R. (2003). A numerical model for the cyclic deterioration of railway tracks. International journal for numerical methods in engineering, 57(4), 441-470. https://doi.org/10.1002/nme.683
• Czyczula, W., Koziol, P., Kudla, D. and Lisowski, S. (2017). Analytical evaluation of track response in the vertical direction due to a moving load. Journal of Vibration and Control. 2017;23(18):2989-3006. doi:10.1177/1077546315625823
• Ngo, N. T., Indraratna, B. and Rujikiatkamjorn, C. (2017). Simulation ballasted track behavior: numerical treatment and field application. International Journal of Geomechanics, 17(6), 04016130. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000831
• Gesualdo, A. and Penta, F. (2018). A model for the mechanical behaviour of the railway track in the lateral plane. International Journal of Mechanical Sciences, 146, 303-318. https://doi.org/10.1016/j.ijmecsci.2018.06.041
• Thambiratnam, D. and Zhuge, Y. (1996). Dynamic analysis of beams on an elastic foundation subjected to moving loads. Journal of sound and vibration, 198(2), 149-169. https://doi.org/10.1006/jsvi.1996.0562
• Heelis, M. E., Collop, A. C., Chapman, D. N. and Krylov, V. (1999). Predicting and measuring vertical track displacements on soft subgrades. In Proceedings of the Railway Engineering—Second International Conference and Exhibition, London, UK, 25–26 May.
• Lu, S., Arnold, R., Farritor, S., Fateh, M. and Carr, G. (2008). On the relationship between load and deflection in railroad track structure. In Proceedings of the AREMA 2008 Annual Conference, Salt Lake City, UT.
• Hendry, M., Hughes, D. A. and Barbour, L. (2010). Track displacement and energy loss in a railway embankment. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 163(1), 3-12. https://doi.org/10.1680/geng.2010.163.1.3
• Sadeghi, J., and Barati, P. (2010). Evaluation of conventional methods in analysis and design of railway track system. International Journal of Civil Engineering, 8(1): 44–55.
• Kumari, S., Sahoo, P. P. and Sawant, V. A. (2012). Dynamic response of railway track using two parameter model. International Journal of Science and Engineering Applications, 1(2), 143-147.
• Prakoso, P. B. (2012). The basic concepts of modelling railway track systems using conventional and finite element methods. Info-Teknik, 13(1), 57-65.
• Mohanta, M., Setu, G., Srivastava, J. P., Sarkar, P. K. and Ranjan, V. (2015). Static analysis of railway track. Proceedings of India International Science Festival. Young Scientists’ Meet, 2015.
• Aksop, E. Y. and Güler, H. (2017). Analysing railway substructure and superstructure by using finite element methods and dimensioning of track components. In 5th International Symposium on Innovative Technologies in Engineering and Science 29-30 September 2017 (ISITES2017 Baku-Azerbaijan).
• Koç, M. A. (2021). Analytic method for vibration analysis of track structure induced by high-speed train. Sakarya University Journal of Science, 25(2), 429-438. https://doi.org/10.16984/saufenbilder.823255
• Lamprea-Pineda, A. C., Connolly, D. P. and Hussein, M. F. (2022). Beams on elastic foundations–A review of railway applications and solutions. Transportation Geotechnics, 33, 100696. https://doi.org/10.1016/j.trgeo.2021.100696
• Yelce, T. U., Balcı, E. and Bezgin, N. Ö. (2023). A discussion on the beam on elastic foundation theory. CHALLENGE, 9(1), 34-47.
• Zhou, J. K. (1986). Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China.
• Agarana, M. C., and Ede, A. N. (2016). Application of differential transform method to vibration analysis of damped railway bridge on Pasternak foundation under moving train. In Proceedings of The World Congress on Engineering and Computer Science. Vol II WCE 2016, June 29 - July 1, 2016, London, U.K.
• Balkaya, M., Kaya, M. O., and Sağlamer, A. (2009). Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method. Archive of Applied Mechanics, 79, 135-146.
• Rajasekaran, S., (2009). Structural dynamics of earthquake engineering: theory and application using mathematica and matlab, India, Woodhead Publishing.
• Bozdoğan, K. B. and Khosravı, F. (2021). Application of differential transformation method and Dunkerley formula for stability analysis of bars in water. Gazi Mühendislik Bilimleri Dergisi, 7(2), 169-174.