Keywords: wavelet theory, vibrations, moving load, viscoelastic solid, beam.

The investigation of the problems vibrations generated by high-speed trains has become a very important subject of research in recent years [1,2]. The theoretical investigations and practical measurements show that the ground vibration boom can appear when the trains move with the velocity even of the order of 200 km/h [1]. This velocity is reached by recent trains leading to dangerous increase of the level of vibrations. Many results concerning railway tracks built on the surface were described in the literature [1,3] whereas some important aspects of modelling of trains moving in the tunnels are still open to investigation.

The theoretical two-dimensional model of a tunnel with a moving load is investigated in this paper. The model consists of two Euler-Bernoulli beams, elastically connected by continuously distributed springs and located parallel to the surface inside the viscoelastic layer. A point load moving along the lower beam is used to simulate a fast moving train problem. Two types of loads were considered: a constant load and a harmonically varying load.

In this paper, complex assumptions were used for modelling leading to a more realistic model than that presented in previous works [4] (half space under the lower beam and different physical properties of layers). The numerical simulations showed that classical methods of numerical integration are not sufficient for the investigation of this model.

A special approximation method based on the wavelet theory [5] was introduced to calculate the components of the displacement vector. This method uses the Coiflet filter coefficients and obtains, without integration, more accurate results using less computational effort than the traditional numerical approach [6].

The main results describe the influence of the damping layer and moving load speed on the level of vibrations at the surface. The critical velocity of the moving load was estimated and approximate displacement values depending on Young's modulus and mass density of the layers were determined. Analytical solutions for the displacements were obtained and discussed.

1

V.V. Krylov (ed.), "Noise and Vibrations from High-Speed Trains", Thomas Telford Ltd, London, 2001.

2

A.V. Metrikine, A.C.W.M. Vrouwenvelder, "Surface ground vibration due to a moving train in a tunnel: two - dimensional model", Journal of Sound and Vibration, 234(1), 43-66, 2000. doi:10.1006/jsvi.1999.2853

3

L. Fryba, "Vibrations of Solids and Structures under Moving Loads", Thomas Telford Ltd., London, 1999.

4

A.V. Metrikine, A.C.W.M. Vrouwenvelder, "Ground vibration induced by a high-speed train in a tunnel: Two-dimensional model", in Wave 2000, Chouw & Schmid (ed.), Balkema, Rotterdam, 111-120, 2000.

5

J. Wang, Y. Zhou, H. Gao, "Computation of the Laplace inverse transform by application of the wavelet theory", Communications in Numerical Methods in Engineering, 19, 959-975, 2003. doi:10.1002/cnm.645

6

P. Koziol, C. Mares, I. Esat, "Wavelet approach for the analysis of surface vibration caused by a train moving in a tunnel", submitted.

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