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Technical Brief

Experimental Nonlinear Model Identification of a Highly Nonlinear Resonator

[+] Author and Article Information
Tanju Yildirim

College of Chemistry and Environmental Engineering,
Shenzhen University,
Shenzhen 518060, China
e-mail: tanjuyildirim1992@hotmail.com

Jiawei Zhang, Shuaishuai Sun

School of Mechanical, Materials and Mechatronic
Engineering,
University of Wollongong,
Northfields Avenue,
Wollongong NSW 2522, Australia

Gursel Alici

School of Mechanical, Materials and Mechatronic
Engineering,
University of Wollongong,
Northfields Avenue,
Wollongong NSW 2522, Australia;
ARC Centre of Excellence for Electromaterials Science,
University of Wollongong,
Innovation Campus,
Wollongong NSW 2522, Australia

Shiwu Zhang

Department of Precision Machinery and Precision
Instrumentation,
University of Science and Technology of China,
Hefei 230026, Anhui, China

Weihua Li

School of Mechanical, Materials and Mechatronic
Engineering,
University of Wollongong,
Northfields Avenue,
Wollongong NSW 2522, Australia
e-mail: weihuali@uow.edu.au

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 23, 2017; final manuscript received November 16, 2017; published online February 9, 2018. Assoc. Editor: A. Srikantha Phani.

J. Vib. Acoust 140(3), 034502 (Feb 09, 2018) (6 pages) Paper No: VIB-17-1031; doi: 10.1115/1.4039030 History: Received January 23, 2017; Revised November 16, 2017

In this work, two model identification methods are used to estimate the nonlinear large deformation behavior of a nonlinear resonator in the time and frequency domains. A doubly clamped beam with a slender geometry carrying a central intraspan mass when subject to a transverse excitation is used as the highly nonlinear resonator. A nonlinear Duffing equation has been used to represent the system for which the main source of nonlinearity arises from large midplane stretching. The first model identification technique uses the free vibration of the system and the Hilbert transform (HT) to identify a nonlinear force–displacement relationship in the large deformation region. The second method uses the frequency response of the system at various base accelerations to relate the maximum resonance frequency to the nonlinear parameter arising from the centerline extensibility. Experiments were conducted using the doubly clamped slender beam and an electrodynamic shaker to identify the model parameters of the system using both of the identification techniques. It was found that both methods produced near identical model parameters; an excellent agreement between theory and experiments was obtained using either of the identification techniques. This follows that two different model identification techniques in the time and frequency domains can be employed to accurately predict the nonlinear response of a highly nonlinear resonator.

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Figures

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Fig. 1

Experimental flowchart

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Fig. 2

Experimentally obtained nonlinear frequency–response curves at various base acceleration (A) (a) dimensional and (b) nondimensional

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Fig. 3

HT results (a) original signal and envelope, (b) instantaneous frequency, and (c) close-up of (b)

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Fig. 4

Proposed nonlinear restoring force per unit mass using HT and free vibration data

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Fig. 5

Comparison of experimental and simulated frequency–response curves using the free vibration method (a) A = 0.1 ms−2, (b) A = 0.2 ms−2, and (c) A = 0.5 ms−2

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Fig. 6

Comparison of experimental and simulated frequency–response curves using the frequency-shift method (a) A = 0.1 ms−2, (b) A = 0.2 ms−2, and (c) A = 0.5 ms−2

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