Dynamics of a semi-infinite beam on unilateral springs: Touch-down points motion and detached bubbles propagation

The dynamics of a semi-infinite Bernoulli–Euler beam laid on a bed of unilateral elastic springs is governed by a moving-boundary problem, since the positions of the touch-down points, those points which separate the detached beam parts from the laid ones, are unknown. This problem is solved numerically by means of a self-made finite element code and some numerical results are shown and discussed. The nonlinear and non-smooth effects of the touch-down points motion on the beams dynamics are analyzed. The presence of detached bubbles, which appear, propagate and disappear in the beam, is investigated, and new complex motions are highlighted.