An examination of multi-frequency excitation of the buckled beam

The dynamics of a magnetically buckled beam excited by a two-frequency forcing function are examined to determine the nature and cause of the system behavior into and outside the parameter range where chaotic oscillations are observed. To facilitate the analysis, the beam is modelled by Duffing's equation with a negative linear stiffness. Bispectral analysis is performed on the trajectories in order to examine the nature and effect of frequency coupling in the motion. Results indicate that varying the relative phase angle of the higher frequency term can result in driving the system in and out of chaos. Bispectral analysis indicates that this controlling behavior of the high-frquency excitation term can be explained by quadratic interactions that transfer energy to the lowest non-linear natural frequency of the beam.