On the Characteristics of Bifurcation and Nonlinear Dynamic Response

[+] Author and Article Information
Baozhong Yang, C. Steve Suh

Mechanical Engineering Department, Texas A&M University, College Station, TX 77843-3123

J. Vib. Acoust 126(4), 574-579 (Dec 21, 2004) (6 pages) doi:10.1115/1.1805007 History: Received July 01, 2003; Revised March 01, 2004; Online December 21, 2004
Copyright © 2004 by ASME
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Kim,  Y. B., and Noah,  S. T., 1991, “Stability and Bifurcation Analysis of Oscillators with Piecewise-Linear Characteristics: A General Approach,” ASME J. Appl. Mech., 58, pp. 545–553.
Huang,  N. E., Shen,  Z., Long,  S. R. , 1998, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis,” Proc. R. Soc. London, Ser. A, A454, pp. 903–995.
Ville, J., 1958, “Theory and Applications of The Notion of Complex Signal,” translated by I. Seline in RAND Technical Report T-92, RAND Corp., Santa Monica, CA.
Cohen, L., 1995, Time-Frequency Analysis, Prentice Hall, Englewood, NJ.
Boashash,  B., 1992, “Estimating and Interpreting the Instantaneous Frequency,” Proc. IEEE, 80, pp. 520–568.
Loughlin,  P. J., and Tacer,  B., 1996, “On the Amplitude- and Frequency-Modulation Decomposition of Signals,” J. Acoust. Soc. Am., 100, pp. 1594–1601.
Gabor,  D., 1946, “Theory of Communications,” IEEE J. Commun. Eng., 93, pp. 429–457.
Yang,  B., and Suh,  C. S., 2003, “Interpretation of Crack-Induced Rotor Nonlinear Response Using Instantaneous Frequency,” Mech. Syst. Signal Process., 18(3), pp. 491–513.
Mayes,  I. W., and Davies,  W. G. R., 1984, “Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor,” ASME J. Vib., Acoust., Stress, Reliab. Des., 106, pp. 139–145.
Yang,  B., Suh,  C. S., and Chan,  A. K., 2002, “Characterization and Detection of Crack-Induced Rotary Instability,” ASME J. Vibr. Acoust., 124(1), pp. 40–48.
Zheng,  T., and Hasebe,  N., 2000, “Nonlinear Dynamics Behavior of a Complex Rotor-Bearing System,” ASME J. Appl. Mech., 67(3), pp. 485–495.
Childs,  D. W., Moes,  H., and van Leeuwen,  H., 1977, “Journal Bearing Impedence Descriptions for Rotordynamic Applications,” ASME J. Lubr. Technol., 99, pp. 198–219.
Dimarogonas,  A. D., 1996, “Vibration of Cracked Structures: A State of the Art Review,” Eng. Fract. Mech., 55(5), pp. 831–857.


Grahic Jump Location
Orbit of journal center at ω=50π rad/s indicating a period-doubling motion
Grahic Jump Location
Variation of instantaneous frequency in response to crack opening and closing
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(a) Time waveform and its IMFs and (b) Instantaneous frequencies for ω=30π rad/s and hr=0.012
Grahic Jump Location
(a) x-y orbit of the journal center at ω=30π rad/s and hr=0.012, (b) Fourier spectrum of the vibration signal in (a)
Grahic Jump Location
(a) Time waveform and its IMFs and (b) instantaneous frequencies for ω=50π rad/s and hr=0.0003 to 0.001.
Grahic Jump Location
(a) Orbit of journal center at ω=50π rad/s and hr=0.09, (b) Fourier spectrum of the vibration signal in (a)
Grahic Jump Location
(a) Time waveform and its IMFs, (b) instantaneous frequencies, and (c) marginal spectrum for ω=50π rad/s and hr=0.06 to 0.09



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