Dynamics of a Quasiperiodically Forced Rayleigh Oscillator

Abstract

This paper studies the dynamics of a self-excited oscillator with two external periodic forces. Both the nonresonant and resonant states of the oscillator are considered. The hysteresis boundaries are derived in terms of the system’s parameters. The stability conditions of periodic oscillations are derived. Routes to chaos are investigated both from direct numerical simulation and from analog simulation of the model describing the forced oscillator. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the system’s behavior. These are of great importance to design engineers. The reliability of the analytical formulas is demonstrated by a very good agreement with the results obtained by both the numeric and experimental analyses.