2_2025_sen_2

Title of the article DYNAMICS OF A RIGID BODY MOVING ON AN ELASTIC BASE WITH A SINGLE POINT OF CONTACT
Authors

MERKURYEV Igor V., D. Sc. in Eng., Prof., Head of the Department of Robotics, Mechatronics, Dynamics and Machine Strength, National Research University “Moscow Power Engineering Institute”, Moscow, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

NAIM Muhannad, Postgraduate Student, National Research University “Moscow Power Engineering Institute”, Moscow, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

SAYPULAEV Gasan R., Ph. D. in Eng., Associate Professor of the Department of Robotics, Mechatronics, Dynamics and Machine Strength, National Research University “Moscow Power Engineering Institute”, Moscow, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section DYNAMICS, DURABILITY OF VEHICLES AND STRUCTURES
Year 2025
Issue 2(71)
Pages 15–21
Type of article RAR
Index UDK 539.384.2
DOI https://doi.org/10.46864/1995-0470-2025-2-71-15-21
Abstract The paper considers the dynamics of a body moving along an elastic beam. The aim of the work is mathematical modeling of the dynamics of the “solid body — elastic beam” system, taking into account the force interaction of these bodies at one point of contact. Based on the Euler–Bernoulli beam theory and general dynamics theorems, partial differential equations of motion of the “solid body — elastic beam” system are constructed. Using the Bubnov–Galerkin method, ordinary differential equations (ODEs) for the weight coefficients of the approximate solution of the partial differential equation are obtained. Based on the results of numerical integration of the ODE, the dependences of the deflection and the angle of rotation of the elastic beam cross section on time are obtained. Unlike the previously used models, the developed model makes it possible to take into account the effect of the force action of a moving solid on the bending of the elastic beam. The results of the work can be used in the design and manufacture of new transport systems.
Keywords dynamics, bending, elastic beam, Bubnov–Galerkin method, Euler–Bernoulli beam
  You can access full text version of the article.
Bibliography
  1. Ivanchenko I.I., Shapovalov S.N. The development of models for high-speed railway track dynamics. Proc. international symposium on speed-up and service technology for railway and maglev systems (STECH’09). Niigata, 2009. DOI: https://doi.org/10.1299/jsmestech.2009._352225-1_.
  2. Ivanchenko I.I., Shapovalov S.N. Design of composite, long structures modeling railway tracks for moving loads. Proc. EUROMECH Colloquium 484 on wave mechanics and stability of long flexible structures subject to moving loads and flows. Delft, 2006, pp. 30–31.
  3. Klasztorny M., Myślecki K., Machelski C., Podwórna M. Dynamic analysis of a series-oftypes of steel beam bridges loaded by a Shinkansen train moving at high speeds. Proc. 5th European conference on structural dynamics EURODYN’2002. Munich, 2002. pp. 1179–1184.
  4. Metrikine A.V., Popp K. Vibration of a periodically supported beam on an elastic half-space. European journal of mechanics – A/Solids, 1999, vol. 18, iss. 4, pp. 679–701. DOI: https://doi.org/10.1016/S0997-7538(99)00141-2.
  5. Zoller V., Zobory I. Analysis of railway track dynamics by using Winkler model with initial geometrical irregularity. Proc. of the 7th mini conference on vehicle system dynamics, identification and anomalies. Budapest, 2000, pp. 113–118.
  6. Kadisov G.M. Dinamika skladchatykh sistem pri podvizhnykh nagruzkakh. Avtoref. diss. dokt. tekhn. nauk [Dynamics of folded systems under moving loads. Abstract of D. Sc. thesis]. Moscow, 1998. 18 p. (in Russ.).
  7. Derendyaev N.V., Soldatov I.N. O dvizhenii tochechnoy massy vdol koleblyushcheysya struny [On the motion of a point mass along an oscillating string]. Journal of applied mathematics and mechanics, 1997, vol. 61, iss. 4, pp. 703–705 (in Russ.).
  8. Kaplunov Yu.D., Muravsky G.B. Deystvie ravnoperemenno dvizhushcheysya sily na balku Timoshenko, lezhashchuyu na uprugom osnovanii. Perekhody cherez kriticheskie skorosti [The effect of an equally alternating moving force on a Timoshenko beam lying on an elastic base. Transitions through critical speeds]. Journal of applied mathematics and mechanics, 1987, vol. 51, iss. 3, pp. 475–482 (in Russ.).
  9. Lu T., Metrikine A.V., Steenbergen M.J.M.M. The equivalent dynamic stiffness of a visco-elastic half-space in interaction with a periodically supported beam under a moving load. European journal of mechanics – A/Solids, 2020, vol. 84. DOI: https://doi.org/10.1016/j.euromechsol.2020.104065.
  10. Kolesov D.A. Volny v odnomernykh raspredelennykh mekhanicheskikh sistemakh, vzaimodeystvuyushchikh s uprugo-inertsionnymi i neodnorodnymi osnovaniyami. Diss. kand. fiz.-mat. nauk [Waves in one-dimensional distributed mechanical systems interacting with elastically inertial and inhomogeneous bases. Ph. D. thesis]. Nizhny Novgorod, 2019. 133 p. (in Russ.).
  11. Leontiev E.V. K voprosu o poperechnykh kolebaniyakh balok na uprugom osnovanii pri izmenenii usloviy opiraniya [Lateral vibrations of beams on an elastic base at changing the supporting conditions]. Building and reconstruction, 2020, vol. 91, no. 5, pp. 70–76. DOI: https://doi.org/10.33979/2073-7416-2020-91-5-70-77 (in Russ.).
  12. Kurbatskiy E.N., Zernov I.I., Badina E.S. Primenenie obobshchennykh funktsiy i integralnogo preobrazovaniya Fure pri modelirovanii vozdeystviya podvizhnoy nagruzki na balku, lezhashchuyu na uprugom osnovanii [Application of generalised functions and Fourier’s integral transformation in modelling the effect of a moving load on a beam resting on an elastic foundation]. Russian journal of transport engineering, 2023, vol. 10, no. 3. DOI: https://doi.org/10.15862/05SATS323 (in Russ.).
  13. Gerasimov S.I., Erofeev V.I., Kolesov D.A., Lisenkova E.E. Dinamika deformiruemykh sistem, nesushchikh dvizhushchiesya nagruzki (obzor publikatsiy i dissertatsionnykh issledovaniy) [Dynamics of deformable systems carrying moving loads (review of publication and dissertation research)]. Bulletin of science and technical development, 2021, no. 160, pp. 25–47. DOI: https://doi.org/10.18411/vntr2021-160-3 (in Russ.).
  14. Afendikova N.G. Istoriya metoda Galerkina i ego rol v tvorchestve M.V. Keldysha [The history of Galerkin’s method and its role in M.V. Keldysh work]. 2014. 16 p. (in Russ.).
  15. Radkovskiy S.A., Trunaev A.M., Poymanov V.D. Modelirovanie kolebaniy zheleznodorozhnogo relsa pri vozdeystvii na nego podvizhnoy vertikalnoy dinamicheskoy nagruzki [Modeling of railway rail vibrations under the influence of a mobile vertical dynamic load on it]. The collection of scientific papers of the Donetsk Railway Transport Institute, 2016, no. 43. Available at: https://clck.ru/3LeS8V (in Russ.).