Normal Mode Uncoupling of Systems with Time Varying Stiffness

Abstract

This paper investigates the conditions for transforming coupled systems with time-varying stiffness to normal mode coordinates. The stability regions are determined from the normal mode equations and the effect of model damping on the width of these regions is investigated. An approximate method for uncoupling is also presented which can be used to give good practical solutions in situations where the theoretical necessary conditions are not met. The proposed method can provide a simple and effective tool for the analysis of parametric vibrations for systems with any number of degrees of freedom as in the case of high speed gear trains.