Rotating machinery has effects of gyroscopic moments, but most of them are small. Then, many kinds of rotor systems satisfy the relation of 1 to $(−1)$ type internal resonance approximately. In this paper, the dynamic characteristics of nonlinear phenomena, especially chaotic vibration, due to the 1 to $(−1)$ type internal resonance at the major critical speed and twice the major critical speed are investigated. The following are clarified theoretically and experimentally: (a) the Hopf bifurcation and consecutive period doubling bifurcations possible route to chaos occur from harmonic resonance at the major critical speed and from subharmonic resonance at twice the major critical speed, (b) another chaotic vibration from the combination resonance occurs at twice the major critical speed. The results demonstrate that chaotic vibration may occur even in the rotor system with weak nonlinearity when the effect of the gyroscopic moment is small.

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