On the mechanisms of vibrational instability in a constrained rotating string

A relatively simple mathematical model involving an idealized rotating stri ng constrained at one point is used to develop an understanding of the basi c physical mechanisms that govern the development of unstable lateral vibra tion response. Equations defining the relationship between the interactive inertial, damping, elastic and applied forces are presented. Analysis of th ese equations leads to a clear understanding of the physical mechanisms inv olved in the development of divergence and flutter instability mechanisms. New developments involve the identification of the energy flux into the rot ating system and an explanation of the role of circumferential forces cause d by interaction with the non-rotating constraint. The equations developed suggest methods for minimizing the instability regions that are encountered in such rotating systems when operating above their lowest critical speed. Numerical examples are presented for the case of a rotating string to illu strate its instability characteristics when constrained by a single degree of freedom viscously damped system. (C) 1999 Academic Press.