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Research Papers

Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments

[+] Author and Article Information
Etienne Gourc, Sébastien Seguy

Institut Clément Ader, INSA,
Université de Toulouse,
Toulouse F-31077, France

Guilhem Michon

Institut Clément Ader, ISAE,
Université de Toulouse,
Toulouse F-31055, France

Alain Berlioz

Institut Clément Ader, UPS,
Université de Toulouse,
Toulouse F-31062, France

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 10, 2014; final manuscript received October 17, 2014; published online January 27, 2015. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 137(3), 031008 (Jun 01, 2015) (7 pages) Paper No: VIB-14-1008; doi: 10.1115/1.4029285 History: Received January 10, 2014; Revised October 17, 2014; Online January 27, 2015

Recently, it has been demonstrated that a vibro-impact type nonlinear energy sink (VI-NES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of an LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equations of motion are analyzed using the method of multiple scales in the case of 1:1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR regimes. A good agreement between theoretical and experimental results is observed.

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References

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Figures

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Fig. 1

Schema of the system

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Fig. 2

Representation of the nonsmooth functions Π(z) and M(z)

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Fig. 3

SIM of the problem for r = 0.6, Δ = 0.015. Straight and dotted lines denote stable and unstable branch of the SIM, respectively. Numerical phase space: (a) stable symmetric 1:1 motion, (b) asymmetric 1:1 motion, and (c) asymmetric 2:2 motion.

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Fig. 4

Illustration of the process of TET under transient loading for λ = 0.95, ε = 0.84%, and Δ = 0.015. (a) and (b) result of numerical integration, (c) 1:1 resonance capture, and (d) projection of the result of numerical integration on the SIM.

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Fig. 5

Case of stable periodic response. Dark and gray lines correspond to the SIM (16) and the curves (23). The circle (o) and cross (+) correspond to stable and unstable fixed points, respectively. Parameters are given in Eq. (24).

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Fig. 6

Numerical integration of Eqs. (4) and (5) for the set of parameters (24) and zoom on the response

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Fig. 7

Case of SMR response. Dark and gray lines correspond to the SIM (16) and the curves (23). The cross (+) corresponds to unstable fixed points. Parameters are given in Eq. (25).

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Fig. 8

Numerical integration of Eqs. (4) and (5) for the set of parameters (25)

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Fig. 9

Picture of the experimental setup. (a) Global view of the system and (b) detailed view of the NES.

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Fig. 10

Experimental and analytical frequency response curves of the LO for G = 0.16 mm (A = 0.019). Dark solid lines correspond to the analytical prediction and gray lines represent the experimental measurements. Straight and dashed lines denote the experimentally and numerically found SMR zone.

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Fig. 11

Experimental measurement of SMR for G = 0.16 mm (A = 0.019) and σ = 1.52

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Fig. 12

Experimental and analytical frequency response curves of the LO for G = 0.14 mm (A = 0.017). Dark lines correspond to the analytical prediction and gray lines represent the experimental measurements. Straight and dashed lines denote the experimentally and numerically found SMR zone.

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Fig. 13

Analytical frequency response curve of the LO for G = 0.125 mm (A = 0.015). Dark lines correspond to the analytical prediction. Straight and dashed lines denote the experimentally and numerically found SMR zone.

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