Qualitative analysis of oscillating magnetomechanical system

Abstract

The paper deals with mathematical modelling and qualitative analysis of a dynamic system of the type mass-spring-permanent magnet. The mass of the system is suspended on the free end of a cantilever beam and oscillates in a magnetic field created by a permanent magnet. The the magnetic force is obtained using the finite element method and approximated by a function similar to the Coulomb’s Law. The dynamical model of the system is built on the basis of the Newton 2nd law. By means of qualitative analysis of a nonlinear differential equation, the bifurcation zones are determined. The phase portraits of the system are investigated depending on its bifurcation behaviour. Based on the performed analysis a method for dynamical synthesis of system parameters is proposed. Besides, some typical properties of the dynamical system are determined.