A Second-Approximation Analysis of the Regions of Parametric Resonances by Taking Damping into Account

Abstract

The present paper deals with the parametric resonances of a viscoelastic system having many degrees of freedom and subjected to a harmonic parametric excitation. The first-order perturbation analysis made by Hsu is extended to the second approximation by introducing the concept of multiple time scales. The main- and sub-regions of parametric resonances are given in explicit forms. The Reut-type system with two degrees of freedom and under a non-canonical periodic load is discussed to demonstrate the usefulness of the present analysis.