The Jeffcott rotor is a two-degree-of-freedom linear model with a disk at the midspan of a massless elastic shaft. This model, executing lateral whirling motions, has been widely used in the linear analyses of rotor vibrations. In the Jeffcott rotor, the natural frequency of a forward-whirling mode and that of a backward-whirling mode have the relation of internal resonance Recently, many researchers analyzed nonlinear phenomena by using the Jeffcott rotor with nonlinear elements. However, they did not take this internal resonance relationship into account. Furthermore in many practical rotating machines, the effect of gyroscopic moments are relatively small. Therefore, the one-to-one internal resonance relationship holds approximately between forward and backward natural frequencies in such machinery. In this paper, nonlinear phenomena in the vicinity of the major critical speed and the rotational speeds of twice and three times the major critical speed are investigated in the Jeffcott rotor and rotor systems with a small gyroscopic moment. The influences of internal resonance on the nonlinear resonances are studied in detail. The following were clarified theoretically and experimentally: (a) the shape of resonance curves becomes far more complex than that of a single resonance; (b) almost periodic motions occur; (c) these phenomena are influenced remarkably by the asymmetrical nonlinearity and gyroscopic moment; and (d) the internal resonance phenomena are strongly influenced by the degree of the discrepancies among critical speeds. The results teach us that the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incorrect results.
Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 2001; final revision, February 2004. Associate Editor: Joseph P. Cusumano.
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Ishida, Y., and Inoue, T. (December 21, 2004). "Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics ." ASME. J. Vib. Acoust. October 2004; 126(4): 476–484. https://doi.org/10.1115/1.1805000
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