Global stability effects of parametric excitation - Karev, Artem; Hagedorn, Peter (Journal of sound and vibration, 2019)
Stability investigations of general non-conservative parametrically excited systems with asynchronous excitation are presented. Focusing on the global stability effects outside of the traditional resonance areas, systems with two degrees of freedom are considered featuring displacement- and/or velocity-proportional parametric excitation with variable phase relations. In particular, facing the lack of studies on this subject, special attention is paid to time-periodic systems containing gyroscopic and circulatory terms. Through the application of the semi-analytical method of normal forms, general conditions for the appearance of possible global effects are derived. Apart from the “total instability” – presently the only known global effect – new stabilizing and destabilizing effects affecting the stability over the whole range of excitation frequencies are discovered. The derived conditions show, that such global effects are expected to be rather common in complex mechanical system, especially those, featuring circulatory terms. The qualitative analytical results are also confirmed by numerical stability analysis based on Floquet theory. As a mechanical example a minimal model of a squealing disk brake is examined. It is shown that this complex model is indeed subject to parametric excitation leading to global stability effects. These findings may contribute to a better understanding of the squealing phenomenon. Further, the newly obtained knowledge may as well be utilized for extended vibration suppression in mechanical systems in the context of parametric anti-resonance.