Averaging in vibration suppression by parametric stiffness excitation (Q840497)

The main purpose of this work is to explore the stability of a self-excited weakly damped system under the influence of a parametric stiffness excitation close to a parametric combination freuqency. First- and second-order averaging of the stability of self-excited and parametrically excited two degrees of freedom systems is investigated. The necessity of a second-order approximation is emphasized for two mechanical example systems that were studied in the literature before. This study explains in great detail how a parametric excitation with a certain freqency, can effectively stabilize a self-excited system that has only a single unstable mode of vibration which corresponds to one negative damping coefficient. The presence of the instability domains raises interesting questions regarding the behaviour of the mechanical models for the corresponding values of the parameters.