Nonlinear oscillations of coupled pendulums subjected to an external magnetic stimulus

The nonlinear forced vibrations of two pendulums coupled by an elastic element are considered. One of the pendulums is subjected to the magnetic stimulus produced by a pair of a periodically powered coil and a permanent magnet mounted at the end of the pendulum. We extend our previous experimental and numerical results presented in Polczynski et al. (2019) and proposed a new rational approximation of a magnetic torque to enable the application of analytical methods. Based on this approximation, the numerical and analytical studies of equations of motion are carried out. In particular, the resonant phenomena and periodic regimes are studied in detail. The procedure to approximate the subharmonic and almost harmonic regimes is developed using the balance harmonic method. The successive maxima map has been employed to study more complicated regimes. This technique allows one to reveal changes in profile's shapes for various driving frequencies and shows the existence of strongly chaotic trajectories. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates the nonlinear forced vibrations of two pendulums coupled by an elastic element, with one pendulum driven by magnetic stimulus. A rational approximation of the magnetic torque enables numerical and analytical studies, focusing on resonant phenomena and periodic regimes. The technique of successive maxima map is employed to study complex regimes, revealing changes in profile shapes and strongly chaotic trajectories at different driving frequencies.