Chaotic dynamics and subharmonic bifurcations of current‐carrying conductors subjected to harmonic excitation

Abstract

AbstractWith both analytical and numerical methods, global dynamics including chaotic motions and subharmonic bifurcations of current‐carrying conductors subjected to harmonic excitation are investigated in this paper. The system parameter conditions for chaos are obtained with the Melnikov method. The monotonicity of the critical value for chaos on the damping, alternating current, and excitation amplitude is studied in detail for three cases. Some interesting dynamic phenomena such as “uncontrollable frequency interval” and “controllable frequency” are presented analytically. Subharmonic bifurcations of odd order or even order are also investigated with the subharmonic Melnikov method. The evolution of subharmonic bifurcation to chaos is studied. It is proved rigorously that the system may undergo chaotic motions through finite or infinite subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold obtained with the analytical method.