Parametric Vibrations of a System of Oscillators Connected with Periodically Variable Stiffness

Abstract

The work is a part of a larger project concerning investigations of different configurations of connected oscillators with direct and parametric forcing sources. Among others, we present preliminary numerical studies of dynamics of a system composed of two oscillators connected with periodically variable stiffness. Each of the oscillators is connected to the fixed support with the use of a nonlinear magnetic spring. Based on the derived mathematical equations of the parametric system, a bifurcation plot was calculated for different shaft speeds. Bifurcation analysis shows both the ranges of periodic and chaotic motion. As an additional part, we will realize this kind of mechanical system from an electrical point of view, and we shall observe the phenomena experimentally.