Keywords: moving load, Euler-Bernoulli beam, viscoelastic foundation, wavelet-based approximation, finite element method.

A modern application of the wavelet analysis is considered by many researchers as a potential source of new ideas for solving engineering problems, particularly related to dynamic systems [1,2]. In the recent years, wavelet-based approaches have been studied in a wide variety of theoretical and applied sciences. One of the subjects important for dynamic analysis of train-track-soil structures is the solving of partial differential equations, where the wavelet-based approximations enable the determination of new analytical and semi-analytical solutions [1,3].

In this paper, the wavelet technique and the classical finite element are explored for the beam response to a load moving along it, while resting on a homogeneous foundation [4,5]. The interaction between the beam and the medium is analyzed in order to obtain the vibration response at the surface.

A comparison between the results from the wavelet technique and those obtained with the classical transient finite element analysis is presented. Some numerical examples with one layer are included. In order to evaluate the effect of important physical parameters on the beam response, the results of simulations are presented for the following parameters: the thickness of the foundation, the viscoelastic properties and the moving load speed. A discussion on the influence of these parameters is presented along with a number of numerical examples.

Finally, some limitations and difficulties of both methods are presented, underlined and discussed. Conclusions from this comparison for the mentioned parametric studies performed are considered useful for the understanding of the differences between these two approaches.

1

P. Koziol, "Wavelet approach for the vibratory analysis of beam-soil structures: dynamically loaded systems", VDM Verlag Dr. Müller, Saarbrucken, 2010.

2

S. Mallat, "A Wavelet Tour of Signal Processing", Academic Press, 1998.

3

P. Koziol, Z. Hryniewicz, "Wavelet based solution for vibrations of a beam on a nonlinear viscoelastic foundation due to a moving load", XII Symposium "The Influence of Vibrations on Environment", Krakow-Janowice, 2010.

4

P. Koziol, Z. Hryniewicz, C. Mares, "Wavelet analysis of beam-soil structure response for fast moving train", Journal of Physics: Conference Series, 181, 012052, 2009, "7th International Conference on Modern Practice in Stress and Vibration Analysis", IOP Publishing, Cambridge, 8-10 September 2009. doi:10.1088/1742-6596/181/1/012052

5

Z. Dimitrovová, J.N. Varandas, "Critical velocity of a load moving on a beam with a sudden change of foundation stiffness: Applications to high-speed trains", Computers and Structures, 87(19-20), 1224-1232, 2009. doi:10.1016/j.compstruc.2008.12.005

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