Vibrations of a Forced Self-Excited System with a Retarded Argument : Influence of Initial Conditions

Abstract

This paper investigates the dynamical characteristics of a forced nonlinear vibrating system with a retarded argument. Entrained subharmonic oscillations of order 1/2 in this system were analyzed, using an averaging scheme. It is clear that almost periodic vibrations and unbounded oscillations besides the subharmonic vibrations, can occur over the frequency region where the entrained subharmonic vibrations of order 1/2 appear, depending upon the initial conditions. Then, as the retarded argument varies, the variety and structure of the boundaries which sepsrate basins of attraction, making use of cell-to-cell mapping and the Poincare mapping method are investigated.