Response of a periodically supported beam on a nonlinear foundation subjected to moving loads

The influence of a nonlinear foundation on the dynamics of a periodically supported beam has been investigated by a novel model. By using Fourier transforms and Dirac comb properties, a relation between the displacement of the beam and the reaction forces of its supports in steady state has been established from the Euler–Bernoulli beam’s equation. This relation holds for any foundation behaviors. Therefore, the dynamic equation of a support has been built by combining this relation and the constitutive law of the foundation and the supports. This equation describes a forced nonlinear oscillator, provided that the moving loads are a periodical series. Then, an iteration procedure has been developed to compute the periodic solution. This procedure has been demonstrated converging to the analytic solution for linear foundations. The applications to bilinear and cubic nonlinear foundations have been performed as examples. Moreover, the influences of nonlinearity on the dynamic responses have been investigated by parametric studies.