Forced Nonlinear Oscillations of a Semi-infinite Beam Resting on a Unilateral Elastic Soil: Analytical and Numerical Solutions

The dynamics of a semi-infinite Eider Bernoulli beam on unilateral elastic springs is investigated. The mechanical model is governed by a moving-boundary hyperbolic problem, which cannot be solved in closed form. Therefore, we look for approximated solutions following two different approaches. Front the one side, approximate analytical solutions are obtained by means of perturbation techniques. On the other side, numerical solutions are determined by a self-mode finite element algorithm. The analytical and numerical solutions are compared with each other, and the effects of the problem non-linearity on the beam motion are analyzed. In particular the superharmonics oscillations and the resonances are investigated in depth.