Modeling and dynamics analysis of a forced two-degree-of-freedom mechanical oscillator with magnetic springs

Abstract

In this paper, oscillations in the physical model consisting of two carts mounted on a guide are considered. The movement of the carts is restricted by the repelling permanent magnets. The interaction between carts is provided by a linear spring. The harmonic external loading is applied to one of the carts. According to the experimental studies, the period doubling cascade leading to the creation of a chaotic attractor occurs with an increase in the forcing frequency in the system. Chaotic attractor crises, quasi-periodic regimes, and finite periodic doubling cascade are revealed as well. To describe system’s dynamics, the nonlinear mathematical model is developed. Based on the experimental data, the procedure of model validation is introduced. The numerical and qualitative analysis of the mathematical model allows one to identify bifurcation types, reveal unstable modes, and discover phenomena existing beyond the main period doubling cascade.