Nonlinear dynamics and snap-through regimes of a bistable buckled beam excited by an electromagnetic Laplace force

Abstract

We study the nonlinear forced dynamics of a bistable buckled beam. Depending on the forcing frequency and amplitude, we observe three different regimes: (i) small intra-well oscillations in the neighborhood of one of the equilibria, (ii) transient snap-through ending into intra-well oscillations, (iii) persistent dynamic snap-through. We build experimentally and numerically phase-diagrams determining the forcing amplitude and frequency leading to each of the three regimes. The experiments leverage an original setup based on the use of the electromagnetic Laplace forces. The controlled flow of an electric current through a metallic beam immersed in an electromagnetic field is at the origin of the electromechanical coupling. This non-invasive excitation system allows us to easily tune the forcing frequency and amplitude. The results of our numerical model, based on a weakly nonlinear geometrical approximation and a three-mode Galërkin expansion for the space discretization, are in excellent agreement with the experimental findings. We show that higher-order modes, often neglected in the modal models of the literature, have a major influence on the nonlinear dynamics.