Averaging in Parametrically Excited Systems - A State Space Formulation

Abstract

Parametric excitation can lead to instabilities as well as to an improved stability behavior, depending on whether a parametric resonance or anti-resonance is induced. In order to calculate the stability domains and boundaries, the method of averaging is applied. The problem is reformulated in state space representation, which allows a general handling of the averaging method especially for systems with non-symmetric system matrices. It is highlighted that this approach can enhance the first order approximation significantly. Two example systems are investigated: a generic mechanical system and a flexible rotor in journal bearings with adjustable geometry.