Asynchronous Parametric Excitation in an Electromechanical System

Abstract

This paper analyzes the effect of asynchronous parametric excitation in an electromechanical system. The system is composed by two interacting subsystems, a mechanical and an electromagnetic. The system does not have elements that can storage potential energies, neither mechanical nor electromagnetic. The system dynamics is written in terms of an inertia matrix M and a gyroscopic matrix G. Two parametric excitation terms are introduced in G. The terms have fixed amplitude, fixed frequency and asynchrony with respect to each other. For different values of the asynchrony, stability maps, in terms of the amplitude and frequency of the parametric excitation, are constructed for the electromechanical system. 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 the asynchrony affects these stability and instability regions.