Abstract
Within this paper problems related with the vibration and stability control of circular flexible shafts spinning about their rotational axis are addressed. Due to the occurrence, as a result of the spinning speed, of gyroscopic forces in the system, the rotating shaft can experience, in some conditions, instabilities of the same nature as any nonconservative system, namely divergence and flutter instabilities. Whereas the former instability is of a static character, the latter one is of dynamic character and the results of its occurrence are catastrophic.
By including collocated sending and actuating capabilities via integration in the system of piezoelectric devices and of a feedback control law, it is shown that a dramatic enhancement of both the free dynamic response and of the stability behavior from both the divergence and flutter points of view can be achieved.
This implies that via the implementation of this technology an increase of the spinning speed can be achieved without the occurrence of these instabilities. Numerical simulations documenting these findings are provided and pertinent conclusions are outlined. It is also worthy to mention that the shaft is modeled as a thin-walled cylinder made of an anisotropic material and incorporating a number of non-classical features.
On the Instability of Stationary Solutions of a Lagrangian System with Gyroscopic Forces