Nonlinear dynamics of two harmonically excited elastic structures with impact interaction

•The dynamics of two elastic structures with impact interaction is investigated.•Discontinuity map is introduced to analyze the stability of period solution.•Experiment is set up to explore the phenomena and verify the numerical results.

In this paper, non-smooth dynamics of two elastic beams excited by harmonic force with impact interaction is studied through analyses, simulations, and experiments. A two degree-of-freedom vibro-impact model is improved by applying the Galerkin approach and Newton's impact law for the two cantilever beams with impact interaction. Numerical analysis is taken to investigate the vibro-impact motions of cantilever beams excited by harmonic force. The l-adding periodic motions and k=1/1, k=2/2, k=3/4, and k=4/4 type of stable periodic motions of the impacted cantilever beam are presented. Poincaré map is established and the Floquet multipliers of the periodic motions are obtained through semi-analytical method to determine the stability of the motions near the bifurcation point. Through associated experiments, typical bifurcations and chaos of the non-smooth system are examined, which are in good agreement with numerical results.