Alyona Lovska, Oleksij Fomin, Anatoliy Horban, Valentyna Radkevych, Pavel Skok, Inna Skliarenko


To ensure the safety of passenger carriages by rail ferries, mathematical modeling of dynamic loading is performed. The accelerations are determined as components of the dynamic load acting on the body of a passenger car. This takes into account the actual hydrometeorological characteristics of the water area of the railway ferry. The calculations are made in relation to the railway ferry "Mukran", which moves the Baltic Sea. The model takes into account that the car body is rigidly fixed relative to the deck and during the oscillations of the railway ferry follows the trajectory of its movement. The solution of the mathematical model is implemented in the Mathcad software environment using the Runge-Kutta method. It is established that the maximum value of the acceleration acting on the car body is 1.8 m/s2.

Determination of the dynamic loading of the passenger car body during transportation by sea is also carried out by computer simulation. The calculations were carried out in the CosmosWorks software package using the finite element method. Numerical values and acceleration distribution fields are obtained relative to the carriage body structure of a passenger car.

A modal analysis of the car body during transportation by rail ferry is carried out. The numerical values of the critical frequencies and waveforms are obtained.

To check the adequacy of the developed models, a calculation is made according to the Fisher criterion. It is established that the hypothesis of adequacy is not rejected.

The research will contribute to the creation of recommendations on the safety of passenger carriages by railway ferries, as well as the manufacture of their modern structures in terms of car-building enterprises.


passenger car; dynamic loading; body acceleration; loading modeling; modal analysis; rail-ferry transportation

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Myamlin, S., Lunys, O., Neduzha, L., Kyryl’chuk, O. (2017). Mathematical Modeling of Dynamic Loading of Cassette Bearings for Freight Cars. Transport Means, 973–976.

Fomin, O. V., Burlutsky, O. V., Fomina, Yu. V. (2015). Development and application of cataloging in structural design of freight car building. Metallurgical and Mining Industry, 2, 250–256.

Lovskaya, A., Ryibin, A. (2016). The study of dynamic load on a wagon–platform at a shunting collision. Eastern-European Journal of Enterprise Technologies, 3 (7 (81)), 4–8. doi:

GOST 34093-2017. Vagonyi passazhirskie lokomotivnoy tyagi. Trebovaniya k prochnosti i dinamicheskim kachestvam (2017). Moscow: Standartinform, 45.

EN 12663-1:2010: Railway applications - Structural requirements of railway vehicle bodies – Part 1: Locomotives and passenger rolling stock (and alternative method for freight wagons) (2010). BSI, 39.

Fomin, O., Lovska, A., Kulbovskyi, I., Holub, H., Kozarchuk, I., Kharuta, V. (2019). Determining the dynamic loading on a semi-wagon when fixing it with a viscous coupling to a ferry deck. Eastern-European Journal of Enterprise Technologies, 2 (7 (98)), 6–12. doi:

Fomin, O., Lovska, A., Masliyev, V., Tsymbaliuk, A., Burlutski, O. (2019). Determining strength indicators for the bearing structure of a covered wagon's body made from round pipes when transported by a railroad ferry. Eastern-European Journal of Enterprise Technologies, 1 (7 (97)), 33–40. doi:

Shimanskiy, Yu. A. (1963). Dinamicheskiy raschet sudovyih konstruktsiy. Leningrad, 444.

Makov, Yu. L. (2007). Kachka sudov. Kaliningrad, 321.

Zemlezin, I. N. (1970). Metodika rascheta i issledovaniya sil, deystvuyuschih na vagon pri transportirovke na morskih paromah. Moscow: Transport, 104.

Lugovskiy, V. V. (1976). Dinamika morya. Leningrad: Sudostroenie, 199.

Klochenko, N. (1988). Parom “Klaypeda”, Morskoy flot, 5, 27–31.

Morskoy zheleznodorozhno-avtomobilno-passazhirskiy parom «Petersburg» (2016). Available at:

Veter i volnyi v okeanah i moryah: spravochnyie dannyih (1974). Leningrad: Transport, 359.

Kiryanov, D. V. (2012). Mathcad 15 / Mathcad Prime 1.0. Saint Petersburg: BHV-Peterburg, 432.

Okorokov, A., Fomin, O., Lovska, A., Vernigora, R., Zhuravel, I., Fomin, V. (2018). Research into a possibility to prolong the time of operation of universal open top wagon bodies that have exhausted their standard resource. Eastern-European Journal of Enterprise Technologies, 3 (7 (93)), 20–26. doi:

Dyakonov, V. (2000). MATHCAD 8/2000: spetsialnyiy spravochnik. Saint Petersburg: Piter, 592.

Alyamovskiy, A. A. (2015). SolidWorks Simulation. Inzhenerniy analiz dlya professionalov: zadachi, metody, rekomendacii. Moscow: DMK Press, 562.

Rudenko, V. M. (2012). Matematychna statystyka. Kyiv: Tsentr uchbovoi literatury, 304.

Matalyckiy, M. A., Hackevich, G. A. (2017). Teoriya veroyatnostey i matematicheskaya statistika. Minsk: Vysheyshaya shkola, 591.

Kosmin, V. V. (2007). Osnovyi nauchnyih issledovaniy. Moscow: GOU “Uchebno-metodicheskiy tsentr po obrazovaniyu na zheleznodorozhnom transporte”, 271.

Kalinina, V. N. (2015). Teoriya veroyatnostey i matematicheskaya statistika. Moscow: Izdatelstvo Yurayt, 472.



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