Revisiting a magneto-elastic strange attractor

We revisit an early example of a nonlinear oscillator that exhibits chaotic motions when subjected to periodic excitation: the magneto-elastically buckled beam. In the paper of Moons and Holmes (1980) [1] magnetic field calculations were outlined but not carried through; instead the nonlinear forces responsible for creation of a two-well potential and buckling were fitted to a polynomial function after reduction to a single mode model. In the present paper we compute the full magnetic field and use it to approximate the forces acting on the beam, also using a single mode reduction. This provides a complete model that accurately predicts equilibria, bifurcations, and free oscillation frequencies of an experimental device. We also compare some periodic, transient and chaotic motions with those obtained by numerical simulations of the single mode model, further illustrating the rich dynamical behavior of this simple electromechanical system.