Resumen
The dynamic analysis of bridges simulated as an Euler-Bernoulli beam models with elastical supports subjected to mobile loads are analyzed by conventional methods to obtain a new solution for displacement. Generally, these beams supports can be characterized by springs with a given stiffness, wich considerably influence the structure dynamic behavior and even attenuate the dynamic amplification.the solutions proposed until now are defined only on span but not on supports.In this paper we use Green's function considering boundary and continuity conditions and shear force to study the global behavior of the beam. A new displacement formulas are proposed for the beam on supports as on span according to the velocity of the mobile load, the beam rigidity as well as the stiffness of supports. A further study leads to present two new formulas which directly gives displacements at the level of supports according only to the beam rigidity and supports stiffness and to the load value at any time. The evolution of support stiffness leads to classical boundary conditions.A study of coupling between the beam and supports is presented, with the study of the comportement in function to the ratio between the beam rigidity and springs stiffness.