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TECHNICAL PAPERS

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

[+] Author and Article Information
Lili Wang

State Key Laboratory of Nonlinear Mechanics (LNM), Chinese Academy of Sciences, and Institute of Applied Physics and Computational Mathematics, Beijing, P.R. China

Jinghui Zhang, Chao Wang, Shiyue Hu

Civil College, Xi’an Jiaotong University, Xi’an, P.R. China

J. Vib. Acoust 125(2), 170-177 (Apr 01, 2003) (8 pages) doi:10.1115/1.1545768 History: Received September 01, 2000; Revised September 01, 2002; Online April 01, 2003
Copyright © 2003 by ASME
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References

Imregun,  M., 1998, “A Survey of Non-linear Analysis Tools for Structural Systems,” Shock Vib. Dig., 30(5), pp. 363–369.
Feldman,  M., 1994, “Non-linear System Vibration Analysis Using Hilbert Transforml. Free Vibration Analysis Method ‘Freevib’,” Mech. Syst. Signal Process., 8(2), pp. 119–127.
Feldman,  M., 1994, “Non-linear System Vibration Analysis Using Hilbert TransformII. Forced Vibration Analysis Method ‘Forcevib’,” Mech. Syst. Signal Process., 8(3), pp. 309–318.
Feldman, M., and Braun, S., 1995, “Identification of Non-linear System Parameters Via the Instantaneous Frequency: Application of the Hilbert Transform and Wigner-Ville Techniques,” Proc., of 13th IMAC, Nashville, TN, pp. 637–642.
Brancaleoni, F., Spina, D., and Valente, C., 1993, “Damage Assessment from the Dynamic Response of Deteriorating Structures,” Safety Evaluation Based Identification Approaches, Natke H. G., Tomlinson G. R., and Yao J. T. P., eds., Braunschweig.
Spina,  D., Valente,  C., and Tomlinson,  G. R., 1996, “A New Procedure for Detecting Non-Linearity From Transient Data Using Gabor Transform,” Nonlinear Dyn., 11, pp. 235–254.
Robertson, A. N., Park, K. C., and Alvin, K. F., 1995, “Extraction of Impulse Response Data Via Wavelet Transform for Structural System Identification,” Proceedings of The Design Engineering Technical Conference, ASME, 84 (1), pp. 1335–1344.
Hyang, S. Y., Qi, G. Z., and Yang, J. C., 1994, “Wavelets for System Identification,” Proc., of 12th IMAC, Honolulu, HI, pp. 1162–1166.
Wang, L., 1999, “The Time-frequency Analysis of Dynamic Systems and its Applications in Non-linear Modelling,” Ph.D. thesis, Xi’an Jiaotong Univ. P.R. China.
Cohen, L., 1995, Time-Frequency Analysis: Theory and Applications, Prentice Hall.
Liu,  G., and Liu,  Z., 1996, “A New Quadratic Time-Frequency Distribution and a Comparative Study of Several Popular Quadratic Time-Frequency Distributions,” J. Electron., 18(5), pp. 455–461.
Andrews, G. E., Askey, R., and Roy, R., 1999, Special Functions, Cambridge University Press, Cambridge.

Figures

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Grayscale view of the modulus of quadratic time-frequency distribution of x(t)
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The Fourier spectrum of x(t)
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The quadratic time-frequency distribution
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The quadratic time-frequency distribution of y(t) (a) α=200 (b) α=0 (c) α=−200
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The elastic force versus displacement
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Damping skeleton curve of a system with square damping
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Damping versus velocity in a system with square damping
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The frequency skeleton curve

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