Dynamics of Continuous Systems Subjected to Traveling Loads


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We studied several cases of dynamical problems, where the motion is driven by a concentrated force or distributed load applied at a moving position. The velocity of motion is assumed as constant. In particular, we studied interactions with periodic structure of the medium. Earlier results on one-dimensional structuresare extended to the case of an array of plates.



Edited by:

Tadeusz Uhl and Andrzej Chudzikiewicz




R. Bogacz, "Dynamics of Continuous Systems Subjected to Traveling Loads", Applied Mechanics and Materials, Vol. 9, pp. 31-40, 2008

Online since:

October 2007





[1] K. Ludwig: Deformation of rail elastically supported of infinite length by loads moving at a constant horizontal velocity. Proc. 5th Int. Congress Appl. Mech., 1938, 650-655.

[2] J.T. Kenney: Steady-state vibrations of beam on elastic foundation for moving load. J Appl. Mech. 4. 21, (1954).

[3] P.M. Mathews: Vibration of beam on elastic foundation. Z. angew. Math. u. Mech. 38. 1958, 105- 115.

[4] R. Bogacz, T. Krzyżyński: On the Bernoulli-Euler beam on a viscoelastic foundation under moving oscillating load. Inst. Fund. Technol. Res. Report Nr 38, 1-40.

[5] R. Bogacz., T. Krzyzynski., K. Popp: Proc. International Symposium on Dynamics of Continua, Eds. D. Besdo and R. Bogacz, Bad Honnef, Shaker Verlag 1998, 55-64.

[6] R. Bogacz, K. Frischmuthb: Mechanical problems with moving load. Scientific papers of Techn. Univ. Radom TRANSPORT 3(23) 2005,. pp.35-42.

[7] A.D. Kerr: The continuously supported rail subjected to axial force and moving load. Int. J. Mech. Sci. 14. 1972. 71-78.

DOI: https://doi.org/10.1016/0020-7403(72)90007-0

[8] R. Bogacz., T. Krzyżynski, K. Popp: On generalization of Mathews' problem of the vibration of a beam on elastic foundation. Z. angew. Math. Mech. 69, 1989, 243-252.

[9] R. Bogacz, Z. Rozenbajgier: Steady state vibration of beam on a visco-elastic semi-space under moving load (in Polish). Proc. of Warsaw Univ. of Technology. 63, (1979), 63-71.

[10] N. Z. Yakushev: Dynamics of elastic systems subjected to dynamic loads. In : Investigation of theory of Plates and Shells. (in Russian). Publ. of Kazan University, (1972).

[11] L. Fryba: Vibration of Solids and Structures under Moving Loads. Groningen, Noordhoff, (1972).

[12] I.D. Achenbach, C.T. Sun: Moving load on flexibly supported Timoshenko beam. Int. J. Solid & Structures. 1. 1965, 353-370.

DOI: https://doi.org/10.1016/0020-7683(65)90001-6

[13] R. Bogacz: On dynamics and stability of continuous systems subjected to distributed moving load. Ing. Archiv. 1983, 57-69.

[14] R. Bogacz, T. Krzyżynski, K. Popp: On vertical and lateral dynamics of periodic guideways for maglev vehicle. Dynamical Problems in Mechanical Systems. Warszawa 1993. 219-233.

[15] Szolc, R. Bogacz, Analysis of the airport runway vibration excited by motion of heavy aircrafts. Proc. of XXII Symposium - Vibration in Physical Systems, Poznań - Będlewo, 2006, pp.343-348.

[16] R. Bogacz, S. Kaliski, Stability of motion of nonlinear oscillators moving along a beam on an elastic foundation, Proc. Vibr. Probl. 4, 5, 1964, pp.279-294.

[17] R. Bogacz, K. Popp, Dynamics and stability of train-track-systems, Proc. of the 2 nd Intern. Conf. on Recent Advances in Structural Dynamics, Southampton 1984, pp.711-726. Study supported by EUREKA Project FOOTPRINT E! 2486.