Internal Resonance in a Rotating Shaft System : The Coincidence of Two Critical Speeds for Subharmonic Oscillation of the Order l/2 and Synchronous Backward Precession

Abstract

We discuss vibration phenomena due to an internal resonance in a symmetrical rotating shaft system with nonlinear spring characteristics. Especially, we treat the case that the critical speeds of a subharmonic oscillation of the order 1/2 and a synchronous backward precession coincide with each other. It is revealed that these two kinds of oscillations are coupled by some kinds of nonlinear components expressed by polar coordinates and that unique shapes of resonance curves appear due to the internal resonance. For example, several resonance curves appear in some rotating speed ranges, the region where the subharmonic oscillation occurs is separated into two parts.