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Research Papers

Experiment-Based Motion Reconstruction and Restitution Coefficient Estimation of a Vibro-Impact System

[+] Author and Article Information
Tao Li

SinoMed LifeTech (Shenzhen) Co., Ltd.,
1505, Block T2, Ali Center,
Shenzhen 518054, Nanshan District, China
e-mail: li_tao_lumiere@126.com

Sébastien Seguy

ICA (Institut Clément Ader), CNRS,
INSA, ISAE, UPS, Mines Albi,
Université de Toulouse,
3 rue Caroline Aigle,
Toulouse F-31077, France
e-mail: seguy@insa-toulouse.fr

Claude-Henri Lamarque

École Nationale des Travaux Publics de l'État,
LTDS UMR CNRS 5513,
Université de Lyon,
3 rue Maurice Audin,
Vaulx-en-Velin Cedex 69518, France
e-mail: claude.lamarque@entpe.fr

Alain Berlioz

ICA (Institut Clément Ader), CNRS,
INSA, ISAE, UPS, Mines Albi,
Université de Toulouse,
3 rue Caroline Aigle,
Toulouse F-31077, France
e-mail: alain.berlioz@univ-tlse3.fr

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 10, 2018; final manuscript received August 26, 2018; published online October 23, 2018. Assoc. Editor: Julian Rimoli.

J. Vib. Acoust 141(2), 021003 (Oct 23, 2018) (8 pages) Paper No: VIB-18-1103; doi: 10.1115/1.4041367 History: Received March 10, 2018; Revised August 26, 2018

The objective of this paper is to demonstrate the motion reconstruction and the parameter estimation of a vibro-impact (VI) system from limited experimental information. Based on the measured displacement and acceleration of its linear main system, the rest motion information such as the displacement and velocity of the attached VI energy sink can be calculated rather than difficult direct measurement, and therefore, different response regimes from the strongly modulated response to the classic regime with two impacts per cycle are reconstructed. Consequently, it provides comprehensive experimental data for the validation of analytical and numerical results and for any experimental bifurcation analysis. Moreover, a procedure to estimate the restitution coefficient from periodic impacts is demonstrated. This new experimental approach to estimate the value of the restitution coefficient is simple and this accurate value could play an important role in analytical and numerical study.

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References

Ibrahim, R. A. , 2009, Vibro-Impact Dynamics: Modeling, Mapping and Applications, Vol. 43, Springer Science & Business Media, Berlin.
Vakakis, A. F. , Gendelman, O. , Bergman, L. , McFarland, D. , Kerschen, G. , and Lee, Y. , 2008, Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, Vol. 156, Springer Science & Business Media, Berlin.
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Nucera, F. , Vakakis, A. F. , McFarland, D. M. , Bergman, L. A. , and Kerschen, G. , 2007, “ Targeted Energy Transfers in Vibro-Impact Oscillators for Seismic Mitigation,” Nonlinear Dyn., 50(3), pp. 651–677. [CrossRef]
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Gourc, E. , Michon, G. , Seguy, S. , and Berlioz, A. , 2015, “ Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments,” ASME J. Vib. Acoust., 137(3), p. 031008. [CrossRef]
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Li, T. , Gourc, E. , Seguy, S. , and Berlioz, A. , 2017, “ Dynamics of Two Vibro-Impact Nonlinear Energy Sinks in Parallel Under Periodic and Transient Excitations,” Int. J. Nonlinear Mech., 90, pp. 100–110. [CrossRef]
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Ahmad, M. , Khairul Azwan, I. , and Mat, F. , 2016, “ Impact Models and Coefficient of Restitution: A Review,” ARPN J. Eng. Appl. Sci., 11(10), pp. 6549–6555. http://www.arpnjournals.org/jeas/research_papers/rp_2016/jeas_0516_4312.pdf

Figures

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Fig. 1

Schema of a LO coupled with a VI NES under periodic excitation

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Fig. 2

Experimental configuration of an LO coupled with a VI NES (ball)

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Fig. 3

Detailed view of an LO and a VI NES

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Fig. 4

Acceleration of LO with b = 9 mm: impact moments are denoted by crosses

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Fig. 5

First return map of impact time difference of the time history of acceleration of LO with b = 9 mm: a line denotes two asymmetrical impacts per cycle

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Fig. 6

Displacement of LO with b = 9 mm: impact moments are denoted by circles

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Fig. 7

Reconstruction of the displacement of VI NES in dotted curve with b = 9 mm: displacement of LO in sine curve is shifted to negative and positive by b, and impact moments are denoted by circles

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Fig. 8

Acceleration of LO with b = 15 mm: impact moments are denoted by crosses [10]

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Fig. 9

Reconstruction of the displacement of VI NES in dotted curve with b = 15 mm: displacement of LO in sine curve is shifted to negative and positive by b and impact moments are denoted by circles

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Fig. 10

Acceleration of LO with b = 17.5 mm: impact moments are denoted by crosses

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Fig. 11

Reconstruction of the displacement of VI NES in dotted curve with b = 17.5 mm: displacement of LO in sine curve is shifted to negative and positive by b and impact moments are denoted by circles

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Fig. 12

Velocity of VI NES with b = 9 mm: impact moments are denoted by circles

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Fig. 13

Estimated velocity of LO with b = 9 mm from displacement in nonsmooth curve and acceleration in smooth curve

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Fig. 14

Velocity of LO before and after impact in crosses with b = 9 mm

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Fig. 15

Schema of corrected velocities after and before impacts

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Fig. 16

Estimated restitution coefficients at the right side in circles and the left side in crosses with b = 9 mm: dotted lines are two corresponding values of root-mean-square

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Fig. 17

Estimated restitution coefficients at the right side in circles and the left side in crosses with b = 7.5 mm: dotted lines are two corresponding values of root-mean-square

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Fig. 18

Estimated restitution coefficients at the right side in circles and the left side in crosses with b = 6 mm: dotted lines are two corresponding values of root-mean-square

Tables

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