The problem under consideration is the dynamic behaviour of this double layer under the action of a moving load.

Figure 78.1: The discrete/continuum halfspace under the action of a moving load.

Suiker and al.[4,5,6,7] have considered one 2D finite and discrete layer resting on a rigid support. Nguyen [3] has proposed a general continuous multilayer modelling with an undetermined layer's number. The ballast's modelling is based on the Lagrange's equations [2]: for that, we postulate a priori a formal distribution of ballast's grains on a simple cubic lattice ([1], Figure 78.1) and formal energy interactions between the nearest grains which depend only on their relative positions. For the discrete/continuous interaction, we consider that grains in contact with the underlayer are embedded in it: continuity of displacement and continuity of force.

The validations of this modelling consist in comparing an infinite discrete ballast's half-space to the analytical Boussinesq's result and to a continuum model. Second order Taylor approximations of the discrete equations are used to identify the discrete lattice parameter with those of a continuum linear elastic isotropic medium.

The influences of the following parameters are studied: the stiffness of the underlayer, the velocity of the moving load, the number of ballast's grains in the vertical direction. A comparison with the continuous modelling [3] will be provided for realistic moving loads.

1

Brillouin L., "Propagation des ondes dans les milieux periodiques", Masson, Paris, 1956.

2

Brousse P., "Mecanique analytique", Vuibert Universite, Paris, 1981,ISBN 2-7117-2205-8.

3

Nguyen V. H., "Comportement dynamique de structures non-lineaires soumises a des charges mobiles.", PhD thesis, Ecole Nationale des Ponts et Chaussees, 2002.

4

Suiker and al. "Dynamic behaviour of a layer of discrete particles, part 1: analysis of body waves and eigenmodes", Journal of Sound and Vibration, vol 240, p. 1-18, 2001. doi:10.1006/jsvi.2000.3202

5

Suiker and al., "Dynamic behaviour of a layer of discrete particles, part 2: response to a uniformly moving, harmonically vibrating load", Journal of Sound and Vibration, vol 240, p. 19-39, 2001. doi:10.1006/jsvi.2000.3203

6

Suiker and al., "Surface waves in a stratified half space with enhanced continuum properties, part 1: Formulation of the boundary value problem.", Eur.J.Mech.A/Solids, vol 18, p. 749-768, 1999. doi:10.1016/S0997-7538(99)00108-4

7

Suiker and al., "Surface waves in a stratified half space with enhanced continuum properties, part 2: Analysis of the wave characteristics in regard to high-speed railway tracks", Eur.J.Mech.A/Solids, vol 18, p. 769-784, 1999. doi:10.1016/S0997-7538(99)00107-2

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