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Research Papers

On Using a Strong High-Frequency Excitation for Parametric Identification of Nonlinear Systems

[+] Author and Article Information
Abdraouf Abusoua

Department of Mechanical Engineering,
Clemson University,
Clemson, SC 29634

Mohammed F. Daqaq

Division of Engineering,
New York University,
Abu Dhabi 129188, United Arab Emirates
e-mail: mfd6@nyu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 17, 2016; final manuscript received April 13, 2017; published online July 10, 2017. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 139(5), 051012 (Jul 10, 2017) (7 pages) Paper No: VIB-16-1507; doi: 10.1115/1.4036504 History: Received October 17, 2016; Revised April 13, 2017

This paper describes a new parametric method for the development of nonlinear models with parameters identified from an experimental setting. The approach is based on applying a strong nonresonant high-frequency harmonic excitation to the unknown nonlinear system and monitoring its influence on the slow modulation of the system's response. In particular, it is observed that the high-frequency excitation induces a shift in the slow-modulation frequency and a static bias in the mean of the dynamic response. Such changes can be directly related to the amplitude and frequency of the strong excitation offering a unique methodology to identify the unknown nonlinear parameters. The proposed technique is implemented to identify the nonlinear restoring-force coefficients of three experimental systems. Results demonstrate that this technique is capable of identifying the nonlinear parameters with relatively good accuracy.

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References

Figures

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Fig. 1

Time history of the free response obtained using N = 3, β1 = 1, ζ = 0.01, β2 = −0.5, and β3 = 1

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Fig. 2

Time histories of the unfiltered response obtained using N = 3, β1 = 1, ζ = 0.01, β2 = −0.5, β3 = 1, and Ω=10β1 : (a) f = 15 and (b) f = 30

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Fig. 3

Time histories of the filtered response obtained using N = 3, β1 = 1, ζ = 0.01, β2 = −0.5, β3 = 1, Ω=10β1, and ωc=5β1 : (a) f = 15 and (b) f = 30

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Fig. 4

Setup used for systems I and II

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Fig. 5

Variation of the natural frequency with the base acceleration for system I

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Fig. 6

Frequency-response curve of system I obtained for a base acceleration of 0.25 m/s2. Dots represent experimental data, and dashed lines represent unstable numerical solutions.

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Fig. 7

Variation of the natural frequency with the base acceleration system II

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Fig. 8

Frequency-response curve of system II obtained for a base acceleration of 0.25 m/s2. Dots represent experimental backward sweep; squares represent experimental forward sweep; and dashed lines represent unstable numerical responses.

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Fig. 9

Setup used for system III

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Fig. 10

Variation of (a) the natural frequency and (b) the static bias with the base acceleration for system III

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Fig. 11

Frequency-response curve of system III obtained for a base acceleration of 0.25 m/s2. Dots represent experimental backward sweep; squares represent experimental forward sweep; and dashed lines represent unstable numerical responses.

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