Keywords: moving load, vibrations, multilayered foundation, wavelet approximation, coiflet filters, generalized coiflets.

In this paper, a two-dimensional theoretical model of a multilayered medium is studied. The model consists of an Euler-Bernoulli beam resting on the surface of a viscoelastic foundation and a distributed load harmonically varying in time, moving along the beam [1]. A method based on a topology optimization, combined with a wavelet expansion of functions [2,3,4], was previously applied by the authors to the problem of seeking the optimal physical and geometrical features of the model [3]. The applied filter of sixth order (of length eighteen) enabled the use of the method for an analysis of the model consisting of two layers. For cases with three or more layers, the developed methodology becomes inefficient as a result of its lack of effectiveness in numerical computations.

It was shown that wavelets defined using coiflet filters are useful in applications where interpolation is of importance [1,2,3,5]. The wavelet-based method using a coiflet expansion of the response, proposed for the evaluation of vibration amplitude in [1,3,5], is tested for various filters associated with generalized coiflets [6]. A specific filter of length eight is found to give similar results to those obtained using the filter considered in the previous publications for simpler systems. A smaller number of filter coefficients makes the numerical computations more effective, enabling the methodology developed to be applied to complex multilayered models. The effectiveness of the new coiflet filter is tested for the model with three layers each possessing different physical properties.

1

P. Koziol, "Wavelet Analysis of Multilayered Ground Vibrations as a Result of High Speed Trains", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 49, 2009. doi:10.4203/ccp.91.49

2

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

3

P. Koziol, M.M. Neves, "Wavelet analysis and optimization technique to improve vibration attenuation for the model of multilayered medium subjected to a load moving along its surface", in N.M.M. Maia, M.M. Neves, R.P.C. Sampaio, (Editors), "ICEdyn2011, International Conference on Engineering Dynamics", 20-22 June 2011, Tavira, Portugal, paper N05, 1-8, 2011.

4

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

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

L. Monzon, G. Beylkin, W. Hereman, "Compactly supported wavelets based on almost interpolating and nearly linear phase filters (coiflets)", Applied and Computational Harmonic Analysis, 7, 184-210, 1999. doi:10.1006/acha.1999.0266

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