Hryniewicz Z.

Solution for vibration of the viscoelastic layer generated by a load moving along a beam inside the layer is derived in analytical form. The displacements are obtained by means of the Fourier integral. The integrand is a complicated function of many parameters and the program in the direct integration approach, to calculate the inverse transform, takes a few hours. In this paper it is shown that the inversion of the Fourier transform can be obtained using wavelet theory. The computational time for the calculation of the displacements based on a coiflets, which are the special kind of wavelets, can be reduced substantially to about 10% in comparison with the direct numerical integration. In order to work with a minimum number of parameters that determine the solution of the problem in hand, the dimensionless formulation has been introduced. The properties of the solution can be investigated quantitatively on the basis of the derived formulae for the displacements using Mathematica system. The calculations are conducted on the basis of coiflet filter coefficients, which can be found in the existing literature with no need of computing mother wavelet in explicit form. The numerical results show that the coiflets approach is efficient and powerful technique.