The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.
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April 2003
Technical Papers
Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves
Lili Wang,
e-mail: wllxxx@yahoo.com.cn
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
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Jinghui Zhang,
Jinghui Zhang
Civil College, Xi’an Jiaotong University, Xi’an, P.R. China
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Chao Wang,
Chao Wang
Civil College, Xi’an Jiaotong University, Xi’an, P.R. China
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Shiyue Hu
Shiyue Hu
Civil College, Xi’an Jiaotong University, Xi’an, P.R. China
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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
e-mail: wllxxx@yahoo.com.cn
Jinghui Zhang
Civil College, Xi’an Jiaotong University, Xi’an, P.R. China
Chao Wang
Civil College, Xi’an Jiaotong University, Xi’an, P.R. China
Shiyue Hu
Civil College, Xi’an Jiaotong University, Xi’an, P.R. China
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Sept. 2000; Revised Sept. 2002. Associate Editor: A. Vakakis.
J. Vib. Acoust. Apr 2003, 125(2): 170-177 (8 pages)
Published Online: April 1, 2003
Article history
Received:
September 1, 2000
Revised:
September 1, 2002
Online:
April 1, 2003
Citation
Wang, L., Zhang , J., Wang , C., and Hu, S. (April 1, 2003). "Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves ." ASME. J. Vib. Acoust. April 2003; 125(2): 170–177. https://doi.org/10.1115/1.1545768
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