Asynchronous Parametric Excitation in Dynamical Systems

In the present contribution, the stability behavior of systems featuring circulatory and gyroscopic terms subject to asynchronous parametric excitation is investigated employing the semi-analytical method of normal forms. First, novel stability patterns are identified revealing global stabilizing and destabilizing effects. More importantly, it is shown that, contrary to the previous knowledge, resonance and anti-resonance may both simultaneously appear in the vicinity of certain resonance frequencies with a particularly steep transition between them. Even for complex systems featuring circulatory terms, these effects can be easily assessed qualitatively and quantitatively using the symbolic expressions derived for the most representative stability features. The results are validated on an electronic system following the simulation-based approach. Finally, with the enhanced understanding of the parametric stability phenomena, two exemplary mechanical systems, including a minimal model of a disk brake, are analyzed.