Keywords: moving mass, inertial moving load, vibrations, Pasternak foundation, wavelet approximation, Euler-Bernoulli beam.

This paper presents a new solution for the vibrations of an Euler-Bernoulli beam on a two-parameter foundation generated by a moving load accompanied by a mass. Recent development of train transportation intensifies research in the area of prediction and attenuation of vibrations generated by vehicles and their influence on surrounding environment. New models and methods of solution are sought for better representation of dynamic phenomena related to train-track-soil interactions [1].

Two important physical models are used in the investigations of beam vibrations caused by moving loads and masses: the Timoshenko beam and the Euler-Bernoulli beam. The published papers usually consider the Winkler elastic foundation model called also a one-parameter model [2]. The analyses performed show that one-parameter models do not reflect sufficiently the continuous characteristics of foundations in practical cases. Therefore two-parameter models are considered for the vibratory analysis of beams subjected to moving loads [3].

Two-parameter models increase complexity and difficulties in parameter estimation. Therefore new approaches to the investigation are required for better analysis of their dynamic behaviour. The analytical solutions for infinite beams subjected to moving load without mass are relatively easy to obtain in many situations and a big number of results can be found in the literature. The analysis of moving mass problem, although widely discussed by the authors, is usually performed numerically and a lack of analytical solutions makes deeper investigation of these models ineffective. The performed simulations show that the developed methods are inconvenient and difficult for practical applications.

The method adopted in the present paper is based on wavelet approximation and leads to the effective algorithm for analysis of vibrations induced by moving mass and moving load [4]. This method uses a wavelet expansion of functions and enables laborious calculation of residues to be avoided. It does not involve numerical integration and therefore gives more accurate results than those presented in the literature, allowing the analysis of important properties of the dynamic system to be investigated. The applied approach shows good efficiency in practical calculations and leads to the parametrical analysis of the considered model.

The originality of the paper is represented by the new wavelet-based semi-analytical solution for the moving mass and the alternative method of solution for the moving load in case of the two-parameter model investigated.

1

B. Hermsworth, "Reducing groundborne vibrations: state of the art study", Journal of Sound and Vibration, 231(3), 703-709, 2000.

2

L. Fryba, "Vibrations of Solids and Structures under Moving Loads", Thomas Telford Ltd., London, 1999. doi:10.1115/1.3423922

3

A.D. Kerr, "Elastic and viscoelastic foundation models", Journal of Applied Mechanics, 31(3), 491-498, 1964. doi:10.1115/1.3629667

4

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

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