Comportement dynamique de structures non-linéaires soumises à des charges mobiles

摘要

The aim of this work is to study the nonlinear dynamic of structures under passages of vehicles. The problem of a multi-layer viscoelastic halfspace under a moving load is firstly solved by a semi-analytical method. It allows to understand the physical phenomena and may be used to valid the more complex approaches established later. Many studies on this problem have been realised but still few of its take into account the non-linearity of materials. These non-linearities, which may be very important in some materials (e.g. the ballast), cause the more important dynamical overloadings. We consider here two kinds of nonlinearity : the nonlinear elastic behaviour and the unilaterality. The structure is studied with simple models in one dimension or more complex in three dimensions. The finite element method is chosen in the analyses. The 1D case involves the problem of an uniaxial bar and the problem of a flexion beam posed on viscoelastic strings system. The 3D case uses a ballast material model which is (nonlinear) elastic in compression and is unilateral in principal directions. As we are interested in the stationary solution, we establish and resolve the finite element equations in the moving coordinates by using of a variable transformation. When the load velocity becomes supersonic, the finite element method is no longer valid and we have to use another approach in which the variable transformation is based on discretizated equations. We show also for the uniaxial model, when the load velocity is between the compression wave velocity and the tension ones, that the shock waves may appear in the stationary state. The obtained results are presented and compared with the linear analysis's ones. These results show the important influences of the nonlinearity on the dynamical response of structures.