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Analytical, numerical and experimental analysis of a self-excited oscillator

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 and the hysteresis domains are defined in terms of the system parameters. Making use of the properties of Hill's equation, we derive the stability conditions of oscillation in the resonant case. Phase portraits are obtained numerically and experimentally. One of the most important contributions of this study is to validate a set of reliable analytical expressions (formulae) describing the system behaviour. These are of great importance for design engineers. The reliability of the analytical formulae is demonstrated by the very good agreement between the results obtained by numerical and experimental analyses.