Influence of asynchronous parametric excitation in stability maps of the simplest electromechanical system

Abstract

. In this paper the influence of asynchronous parametric excitation in stability maps of the simplest electromechanical system is analyzed. The system is composed by two interacting subsystems, a mechanical and an electromagnetic, and it has the minimum number of elements necessary to be classified as an electromechanical system. The system does not have elements that can store potential energies, neither mechanical nor electromagnetic. The system dynamics is written in terms of 2 × 2 inertia matrix M and gyroscopic matrix G . Two parametric excitation terms are introduced in G . The terms have an amplitude ϵ , frequency Ω and asynchrony with respect to each other θ . For different values of θ , stability maps, in terms of ϵ and Ω, are constructed for the electromechanical system with the parametric excitation. In each map, it can be seen stability and instability regions of the trivial solution (system’s equilibrium) of the system. The objective of the paper is to analyze how the value of θ affects these stability and instability regions.