On the dynamics of a finite pre-strained bi-layered slab resting on a rigid foundation under the action of an oscillating moving load

This paper investigates the dynamic response of a finitely pre-strained bi-layered slab resting on a rigid foundation to a time-harmonic oscillating moving load, within the scope of the piecewise-homogeneous body model utilizing the 3D linearized wave propagation theory in the initially stressed body. It is assumed that the materials of the layers are highly elastic ones and their elasticity relations are given in terms of the harmonic potential. Moreover, it is also assumed that the velocity of the line-located time-harmonic oscillating moving load is constant as it acts on the free face of the upper layer of the slab. Our investigations were carried out for a 2D problem (plane-strain state) under subsonic velocity for a moving load in complete contact conditions. The corresponding numerical results were obtained for the stiff upper layer and soft lower layer system in which the constants of elasticity for the upper layer material are greater than those of the lower layer material. Numerical results are presented and discussed for the critical velocity and stress distribution for various values of the problem parameters. In particular, it is established that with the oscillating frequency of the moving load, the values of the critical velocity decrease. Moreover, it is established that the initial stretching of the upper layer of the slab causes the critical velocity to increase and the absolute values of the normal stresses acting on the mid-planes of the layers of the slab to decrease.