Keywords: moving load, wavelet approximation, critical velocity, vibrations.

This paper presents the wavelet based approach for analysis of a solid's vibrations as a result of a high speed train. Two two-dimensional models are analysed: the case with a load moving along a beam resting on a surface and the model related to a tunnel with the beam placed in the solid. The theoretical model is described by the Euler-Bernoulli equation for the beam and Navier's elastodynamic equation of motion for the viscoelastic soil. The supporting multilayered medium has infinite thickness and its layers have different physical properties.

A special method based on wavelet expansion [1,2] of functions in a transform domain is adopted for calculation of displacements in the physical domain. This wavelet approximation is effective when one deals with complex dynamic systems [1,3] and allows parametric analysis of the models investigated for load frequencies generated by trains approaching critical velocities. The effectiveness of the method applied is discussed for different systems of parameters in relation to the numerical variations appearing in the simulations. A modified coiflet filter used in the calculations improves an accuracy of the adopted wavelet based method.

Critical velocities are numerically estimated for both models depending on the properties of the solid for the moving load represented by a finite series of distributed harmonic loads. The analysis in the physical domain is carried out for different systems of parameters related to real situations and the discussion of results with regard to critical velocities is presented in the time-velocity domain.

The original contribution of this article is represented by the use of the wavelet approach for the analysis of multilayered models, the derivation of critical velocities for the finite series of distributed harmonic loads and the investigation of the structure response for the type of load considered. The complexity of the investigated multilayered models prevents effective analysis by using classical methods of numerical integration which might give the wrong results for some systems of parameters. The adopted wavelet method avoids numerical integration, leading to relatively simple algorithms for the evaluation of displacements and gives the possibility of the effective numerical simulations. The wavelet approach can be successfully used for parametric analysis of complex dynamic systems with numerical instabilities.

1

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

2

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

3

P. Koziol, C. Mares, "Wavelet analysis of beam-soil structure response for fast moving train", 7th International Conference on Modern Practise in Stress and Vibration Analysis, Cambridge, MPSVA2009, 8-10 September 2009.

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