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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 98
PROCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON RAILWAY TECHNOLOGY: RESEARCH, DEVELOPMENT AND MAINTENANCE
Edited by: J. Pombo
Paper 116

An Analysis of the Dynamic Effects of Periodic Structures subject to a Moving Load

R. Bogacz1, T. Krzyzynski2 and P. Koziol3

1Faculty of Civil Engineering, Cracow University of Technology, Poland
2Institute of Mechatronics, Nanotechnology and Vacuum Technique, 3Department of Civil and Environmental Engineering,
Koszalin University of Technology, Poland

Full Bibliographic Reference for this paper
R. Bogacz, T. Krzyzynski, P. Koziol, "An Analysis of the Dynamic Effects of Periodic Structures subject to a Moving Load", in J. Pombo, (Editor), "Proceedings of the First International Conference on Railway Technology: Research, Development and Maintenance", Civil-Comp Press, Stirlingshire, UK, Paper 116, 2012. doi:10.4203/ccp.98.116
Keywords: railway mechanics, contact problem, wave generation, oscillations, wavelet-based approximation.

Summary
In a number of previous papers devoted to the dynamics of periodical structures under a moving force, various types of oscillations were studied. The dynamic behaviour of uniform structures under a moving force was considered [1]. In this paper, several cases of dynamic problems are studied, where the motion is driven by a concentrated force moving with a constant speed along one-dimensional periodic structures. The common factor of these problems is the appearance of "stopping" and "passing bands" phenomena [2]: excitations with certain frequencies propagate through the whole periodic structure, while others have only a localized effect near the moving source. A high number of periodic cells of the structure need to be studied. Therefore one should find analytical tools that allow a reduction of the numerical computations.

One of approaches proposed for a dynamic analysis of beam-foundation structures is a wavelet-based method using a coiflet expansion of the response. This computationally efficient tool can be used for the estimation of displacements and leads to formulas allowing an effective parametric analysis [3]. It allows the omission of numerical integration and provides the possibility of a more detailed discussion [4,5].

For periodic structures, first a single beam supported by a viscoelastic Winkler foundation is analysed. The beam is subjected to a moving and oscillating concentrated force with a constant velocity [6]. The explanation of why the proper solution was not obtained in the paper [1] is provided. The case of a moving distributed load acting on the Rayleigh beam and the Timoshenko beam shows a specific feature that was not described in [7].

References
1
P.M. Mathews, "Vibration of beam on elastic foundation", Z. angew. Math. u. Mech., 38, 105-115, 1958. doi:10.1002/zamm.19580380305
2
R. Bogacz, T. Krzyzynski, K. Popp, "Wave propagation in two dynamically coupled periodic systems", in D. Besdo, R. Bogacz, (Editors), Proc. International Symposium on Dynamics of Continua, Shaker Verlag, 55-64, 1998.
3
P. Koziol, "Wavelet approach for the vibratory analysis of beam-soil structures: dynamically loaded systems", VDM Verlag Dr. Müller, Saarbrucken, 2010.
4
P. Koziol, C. Mares, I. Esat, "Wavelet approach to vibratory analysis of surface due to a load moving in the layer", International Journal of Solids and Structures, 45, 2140-2159, 2008. doi:10.1016/j.ijsolstr.2007.11.008
5
P. Koziol, C. Mares, "Wavelet approach for vibration analysis of fast moving load on a viscoelastic medium", Shock and Vibration, 17(4-5), 461-472, 2010.
6
R. Bogacz, T. Krzyzynski, K. Popp, "On generalization of Mathews' problem of the vibration of a beam on elastic foundation", Z. angew. Math. Mech., 69, 243-252, 1989. doi:10.1002/zamm.19890690804
7
I.D. Achenbach, C.T. Sun, "Moving load on flexibly supported Timoshenko beam", Int. J. Solid and Structures, 1, 353-370, 1965. doi:10.1016/0020-7683(65)90001-6

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