Self-Excited Vibration in Flexible Rotating Disks Subjected to Various Transverse Interactive Forces: A General Approach

A generalized approach to predict the physical instability mechanisms that are involved in the interaction between a rotating flexible disk and a stationary constraining system is developed. Based upon equations derived for an energy flux analysis, unified instability conditions for various lateral interactive forces are presented. These developments lead to a clear understanding of the physical mechanisms involved in the development of vibrational instabilities. New developments also involve the stability analysis of a rotating disk subjected to multiple moving concentrated regenerative and follower interactive forces that act over a space-fixed sector. The lateral regenerative interactive forces that are responsible for self-excited vibrations in saw-blade cutting are identified and modeled. The generalized Fourier series method is proposed to develop a characteristic equation for time-varying dynamic systems with or without time lag. The resulting equation can be solved efficiently by using Mu¨ller’s algorithm with deflation.