Forced oscillations in the vicinities of both the major and the secondary critical speeds of a continuous asymmetrical rotor with the geometric nonlinearity are discussed. When the self-aligning double-row ball bearings support the slender flexible rotor at both ends, the geometric nonlinearity appears due to the stiffening effect in elongation of the shaft if the movements of the bearings in the longitudinal direction are restricted. The nonlinearity is symmetric when the rotor is supported vertically, and is asymmetric when it is supported horizontally. Because the rotor is slender, the natural frequency of a forward whirling mode and of a backward whirling mode have the relation of internal resonance . Due to the influence of the internal resonance, various phenomena occur, such as Hopf bifurcation, an almost periodic motion, the appearance of new branches, and the diminish of unstable region. These phenomena were clarified theoretically and experimentally. Moreover, this paper focuses on the influences of the nonlinearity, the unbalance, the damping, and the lateral force on the vibration characteristics.
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e-mail: nagasaka@isc.chubu.ac.jp
e-mail: ishida@nuem.nagoya-u.ac.jp
e-mail: liu@nuem.nagoya-u.ac.jp
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June 2008
Research Papers
Forced Oscillations of a Continuous Asymmetrical Rotor With Geometric Nonlinearity (Major Critical Speed and Secondary Critical Speed)
Imao Nagasaka,
Imao Nagasaka
Department of Mechanical Engineering,
e-mail: nagasaka@isc.chubu.ac.jp
Chubu University
, Aichi 487-8501, Japan
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Yukio Ishida,
Yukio Ishida
Department of Mechanical Science and Engineering, School of Engineering,
e-mail: ishida@nuem.nagoya-u.ac.jp
Nagoya University
, Nagoya, Aichi 464-8603, Japan
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Jun Liu
Jun Liu
Department of Mechanical Science and Engineering, School of Engineering,
e-mail: liu@nuem.nagoya-u.ac.jp
Nagoya University
, Nagoya, Aichi 464-8603, Japan
Search for other works by this author on:
Imao Nagasaka
Department of Mechanical Engineering,
Chubu University
, Aichi 487-8501, Japane-mail: nagasaka@isc.chubu.ac.jp
Yukio Ishida
Department of Mechanical Science and Engineering, School of Engineering,
Nagoya University
, Nagoya, Aichi 464-8603, Japane-mail: ishida@nuem.nagoya-u.ac.jp
Jun Liu
Department of Mechanical Science and Engineering, School of Engineering,
Nagoya University
, Nagoya, Aichi 464-8603, Japane-mail: liu@nuem.nagoya-u.ac.jp
J. Vib. Acoust. Jun 2008, 130(3): 031012 (7 pages)
Published Online: May 14, 2008
Article history
Received:
August 12, 2006
Revised:
October 26, 2006
Published:
May 14, 2008
Citation
Nagasaka, I., Ishida, Y., and Liu, J. (May 14, 2008). "Forced Oscillations of a Continuous Asymmetrical Rotor With Geometric Nonlinearity (Major Critical Speed and Secondary Critical Speed)." ASME. J. Vib. Acoust. June 2008; 130(3): 031012. https://doi.org/10.1115/1.2890734
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