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Research Papers

Stiffness Sensor for Cubic Nonlinear Elasticity Using Nonlinear Self-Excited Oscillation

[+] Author and Article Information
Yosuke Kokubun

Graduate Student
Department of Mechanical Engineering,
Keio University,
3-14-1 Hiyoshi,
Kouhoku, Yokohama City,
Kanagawa 223-8522, Japan

Hiroshi Yabuno

Professor
Graduate School of Systems
and Information Engineering,
University of Tsukuba,
1-1-1, Ten-no-dai,
Tsukuba Science City,
Ibaraki 305-8573, Japan
e-mail: yabuno@esys.tsukuba.ac.jp

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 13, 2013; final manuscript received February 5, 2014; published online April 1, 2014. Assoc. Editor: Steven W Shaw.

J. Vib. Acoust 136(3), 031011 (Apr 01, 2014) (5 pages) Paper No: VIB-13-1200; doi: 10.1115/1.4026889 History: Received June 13, 2013; Revised February 05, 2014

The present paper develops a nonlinear stiffness sensor for measuring cubic nonlinear elasticity. The measurement system consists of a vibrator with a control circuit. We apply linear-plus-nonlinear feedback to actuate the vibrator attached to a measurement object for inducing van der Pol type self-excited oscillation so that the response amplitude of the oscillation can be set arbitrarily by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity of the measurement object causes a natural frequency shift related to the magnitude of vibration amplitude of the vibrator. We can set the response amplitude to various values by changing the nonlinear feedback gain and measuring the shift of the response frequency depending on the magnitude of the response amplitude. As a result, based on the bend of the experimentally obtained backbone curve, the nonlinear elasticity of the measurement object is identified.

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Figures

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Fig. 1

Schematic diagram of the measurement system. The control force is applied to the measurement object through a vibrator, and a van der Pol type self-excited oscillation is produced in the vibration rod attached to the measurement object under the proposed nonlinear feedback control.

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Fig. 2

Backbone curves of the vibration rod attached to the measurement object. expressed by ω = 1+Klin+(3Knon/81+Klin), where ω is the nonlinear natural frequency depending on the amplitude. Klin and Knon are the linear stiffness and the nonlinear stiffness of the measurement object. Knon is positive or negative depending on whether the nonlinear characteristic of the measurement object is hard or soft, respectively. The backbone curve corresponds to the relationship between the response frequency and the response amplitude in the van der Pol type self-excited vibration rod.

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Fig. 3

Experimental apparatus for measuring the nonlinear stiffness using the proposed measurement method. The nonlinear stiffness is caused by the repulsive forces in two pairs of permanent magnets.

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Fig. 4

Picture of experimental apparatus for measuring the nonlinear stiffness using the proposed measurement method

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Fig. 5

Frequency response curve. The plots show the relationship between the response frequency and the response amplitude, which is set to various values by changing the nonlinear feedback gain. The line is the curve fitted by the least squares method.

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Fig. 6

Static measurement of nonlinear stiffness of the measurement object by digital force gauge

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Fig. 7

Relationship between displacement and magnetic restoring force. The line is the curve obtained using klin and knon identified from the proposed measurement method, and klin = 2.19 and knon = 0.0057 are estimated from Fig. 5. The plots indicate the values obtained by static measurement.

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