Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

Yukio Ishida; Tsuyoshi Inoue

doi:10.1115/1.1805000

Journal of Vibration and Acoustics | Volume 126 | Issue 4 | TECHNICAL PAPERS

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TECHNICAL PAPERS

Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

Yukio Ishida and Tsuyoshi Inoue

[+] Author and Article Information

Yukio Ishida, Tsuyoshi Inoue

Department of Electronic-Mechanical Engineering, School of Engineering, Nagoya University, Nagoya, Aichi, 464-8603, Japan

J. Vib. Acoust 126(4), 476-484 (Dec 21, 2004) (9 pages) doi:10.1115/1.1805000 History: Received February 01, 2001; Revised February 01, 2004; Online December 21, 2004

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References

Ehrich, F. F., 1988, “High Order Subharmonic Response of High Speed Rotors in Bearing Clearance,” ASME J. Vib., Acoust., Stress, Reliab. Des., 110, pp. 9–16.

Kim, Y. B., and Noah, S. T., 1990, “Bifurcation Analysis for a Modified Jeffcott Rotor With Bearing Clearance,” Nonlinear Dyn., 1, pp. 221–241.

Sethna, P. R., 1960, “Steady-State Undamped Vibrations of a Class of Nonlinear Discrete Systems,” ASME J. Appl. Mech., 27-1, pp. 187–195.

Nayfeh, A. H., and Balachandran, B., 1989, “Modal Interactions in Dynamical and Structural Systems,” ASME J. Appl. Mech., 42-11-2, pp. 175–201.

Yamamoto, T., and Ishida, Y., 1977, “Theoretical Discussions on Vibrations of a Rotating Shaft With Nonlinear Spring Characteristics,” Ingenieur-Archiv,46, pp. 125–135.

Yamamoto, T., 1957, “On the Vibrations of a Rotating Shaft,” Memoirs of the Faculty of Engineering, Nagoya Univ. 9-1 , pp. 19–115.

Yamamoto, T., Ishida, Y., and Ikeda, T., 1985, “Super-Summed-and-Differential Harmonic Oscillations in a Symmetrical Rotating Shaft System,” Bulletin of the JSME 28-238 , pp. 679–686.

Stoker, J. J., 1950, “Nonlinear Vibrations in Mechanical and Electrical Systems,” John Wiley and Sons, New York.

Yamamoto, T., and Yasuda, K., 1977, “On the Internal Resonance in a Nonlinear Two-Degree-of-Freedom System (Forced Vibrations Near the Lower Resonance Point When the Natural Frequencies are in the Ratio 1:2),” Bulletin of the JSME 20-140 , pp. 168–175.

Ishida, Y., 1994, “Nonlinear Vibrations and Chaos in Rotordynamics,” JSME Int. J., Ser. C, 37-2, pp. 237–245.

Figures

Natural frequencies: (a) The Jeffcott rotor; (b) 2-dof inclination model

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Resonance curves of the Jeffcott rotor (the major critical speed) (i_p=0.0)

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Time histories and spectra (the major critical speed): (a) Steady-state oscillation (ω=1.0); (b) Almost-periodic motion (ω=1.17)

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Analytical model: (a) The Jeffcott rotor; (b) 2-dof inclination model

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Experimental results (three times the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 3)

View Large | Save Figure | Download Slide (.ppt)

Time histries and spectra (three times the major critical speed, experimental results): (a) Steady-state oscillation (Setup 1); (b) Almost-periodic motion (setup 3)

View Large | Save Figure | Download Slide (.ppt)

Resonance curves of the rotor with discrepancy among critical speeds (the major critical speed): (a) Slight discrepancies; (b) Small discrepancies

View Large | Save Figure | Download Slide (.ppt)

Resonance curves of the Jeffcott rotor (twice the major critical speed)

View Large | Save Figure | Download Slide (.ppt)

Resonance curves of the rotor with discrepancies among critical speeds (at twice the major critical speed): (a) Slight discrepancies; (b) Time histories and spectra; (c) Small discrepancies

View Large | Save Figure | Download Slide (.ppt)

Resonance curves of the Jeffcott rotor (three times the major critical speed): (a) ε⁽¹⁾=0.1; (b) Time histories and spectra; (c) ε⁽¹⁾=0.055

View Large | Save Figure | Download Slide (.ppt)

Resonance curves of the rotor with discrepancies among critical speeds (three times the major critical speed)

View Large | Save Figure | Download Slide (.ppt)

Experimental system: (a) Setup; (b) Natural frequencies

View Large | Save Figure | Download Slide (.ppt)

Experimental results (the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 4)

View Large | Save Figure | Download Slide (.ppt)

Time histries and spectra (the major critical speed, experimental results): (a) Steady-state oscillation (Setup 1); (b) Almost-periodic motion (Setup 4)

View Large | Save Figure | Download Slide (.ppt)

Experimental results (twice the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 2)

View Large | Save Figure | Download Slide (.ppt)

Time histories and Spectra (twice the major critical speed, experimental results): (a) Steady-state oscillation (1491 rpm); (b) Almost-periodic motion (1458 rpm)

View Large | Save Figure | Download Slide (.ppt)

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Ishida Y, Inoue T. Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics. ASME. J. Vib. Acoust. 2004;126(4):476-484. doi:10.1115/1.1805000.

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Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

References

Figures

Natural frequencies: (a) The Jeffcott rotor; (b) 2-dof inclination model

Resonance curves of the Jeffcott rotor (the major critical speed) (i_p=0.0)

Time histories and spectra (the major critical speed): (a) Steady-state oscillation (ω=1.0); (b) Almost-periodic motion (ω=1.17)

Analytical model: (a) The Jeffcott rotor; (b) 2-dof inclination model

Experimental results (three times the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 3)

Time histries and spectra (three times the major critical speed, experimental results): (a) Steady-state oscillation (Setup 1); (b) Almost-periodic motion (setup 3)

Resonance curves of the rotor with discrepancy among critical speeds (the major critical speed): (a) Slight discrepancies; (b) Small discrepancies

Resonance curves of the Jeffcott rotor (twice the major critical speed)

Resonance curves of the rotor with discrepancies among critical speeds (at twice the major critical speed): (a) Slight discrepancies; (b) Time histories and spectra; (c) Small discrepancies

Resonance curves of the Jeffcott rotor (three times the major critical speed): (a) ε⁽¹⁾=0.1; (b) Time histories and spectra; (c) ε⁽¹⁾=0.055

Resonance curves of the rotor with discrepancies among critical speeds (three times the major critical speed)

Experimental system: (a) Setup; (b) Natural frequencies

Experimental results (the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 4)

Time histries and spectra (the major critical speed, experimental results): (a) Steady-state oscillation (Setup 1); (b) Almost-periodic motion (Setup 4)

Experimental results (twice the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 2)

Time histories and Spectra (twice the major critical speed, experimental results): (a) Steady-state oscillation (1491 rpm); (b) Almost-periodic motion (1458 rpm)

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

References

Figures

Natural frequencies: (a) The Jeffcott rotor; (b) 2-dof inclination model

Resonance curves of the Jeffcott rotor (the major critical speed) (ip=0.0)

Time histories and spectra (the major critical speed): (a) Steady-state oscillation (ω=1.0); (b) Almost-periodic motion (ω=1.17)

Analytical model: (a) The Jeffcott rotor; (b) 2-dof inclination model

Experimental results (three times the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 3)

Time histries and spectra (three times the major critical speed, experimental results): (a) Steady-state oscillation (Setup 1); (b) Almost-periodic motion (setup 3)

Resonance curves of the rotor with discrepancy among critical speeds (the major critical speed): (a) Slight discrepancies; (b) Small discrepancies

Resonance curves of the Jeffcott rotor (twice the major critical speed)

Resonance curves of the rotor with discrepancies among critical speeds (at twice the major critical speed): (a) Slight discrepancies; (b) Time histories and spectra; (c) Small discrepancies

Resonance curves of the Jeffcott rotor (three times the major critical speed): (a) ε(1)=0.1; (b) Time histories and spectra; (c) ε(1)=0.055

Resonance curves of the rotor with discrepancies among critical speeds (three times the major critical speed)

Experimental system: (a) Setup; (b) Natural frequencies

Experimental results (the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 4)

Time histries and spectra (the major critical speed, experimental results): (a) Steady-state oscillation (Setup 1); (b) Almost-periodic motion (Setup 4)

Experimental results (twice the major critical speed): (a) The Jeffcott rotor (setup 1); (b) Rotor with discrepancies among critical speeds (setup 2)

Time histories and Spectra (twice the major critical speed, experimental results): (a) Steady-state oscillation (1491 rpm); (b) Almost-periodic motion (1458 rpm)

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

Resonance curves of the Jeffcott rotor (the major critical speed) (i_p=0.0)

Resonance curves of the Jeffcott rotor (three times the major critical speed): (a) ε⁽¹⁾=0.1; (b) Time histories and spectra; (c) ε⁽¹⁾=0.055