Resonances and Synchronization in Two Coupled Oscillators with Stick-Slip Vibrations and Spring Pendulums

Abstract

We study the dynamical behavior of a system of two coupled mechanical oscillators with spring pendulums and driven by a stick-slip induced vibrations. Each of the oscillator consists of the body placed onto a moving belt/foundation, mechanical coupling associated with the body load pressed the belt depending on the body movement as well as suspended spring pendulum. In addition, the influence of the presence of additional electric/electromagnetic forces acting on the pendulums are analyzed. Different kinds of resonance behavior can be found in the studied system, even if it is simplified to a single degree-of-freedom system. As a result, due to many degrees-of-freedom and strong nonlinearity and discontinuity of the considered system, novel nonlinear dynamical phenomena occur, both near and beyond to the resonance. The motion analysis for different cases is carried out by employing standard numerical methods dedicated for nonlinear systems, including both qualitative and quantitative methods, as well as original animations of the system dynamics created in Mathematica. Understanding the role of coupling, transition between fixed points and energy transition in the considered system can be potentially applied in other similar systems, especially in real electro-mechanical systems, power system or in structural engineering