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RESEARCH PAPERS

Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments

[+] Author and Article Information
Joël Perret-Liaudet

Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, UMR 5513, F-69134 Ecully cedex, Francejoel.perret-liaudet@ec-lyon.fr

Emmanuel Rigaud

Laboratoire de Tribologie et Dynamique des Systèmes, Ecole Centrale de Lyon, UMR 5513, F-69134 Ecully cedex, Franceemmanuel.rigaud@ec-lyon.fr

J. Comput. Nonlinear Dynam 2(2), 190-196 (Dec 21, 2006) (7 pages) doi:10.1115/1.2447549 History: Received November 22, 2005; Revised December 21, 2006

The purpose of this paper is to investigate experimental responses of a preloaded vibroimpact Hertzian contact to an order 2 superharmonic excitation. A test rig is used, corresponding to a double sphere–plane contact preloaded by the weight of a moving body. Typical response curves are obtained under the superharmonic excitation. The Hertzian nonlinearity constitutes the precursor of vibroimpacts established over a wide frequency range. This behavior can be related to the existence of a transcritical bifurcation. In conjuction with the experiments, numerical results lead to the same conclusion. In particular, the threshold level of the excitation necessary to induce vibroimpact is confirmed.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Dynamic model of the SDOF impact oscillator

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Figure 2

The experimental test rig

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Figure 3

Magnitudes of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=24.5%): stable responses (thick line); unstable responses (thin line); experimental results (σ=28.5%) (square).

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Figure 4

Phases of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=24.5%): stable responses (thick line); unstable responses: (thin line); experimental results (σ=28.5%) (square).

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Figure 5

Frequency response curve of the magnitude A defined by Eq. 23. Multiple scales method (σ=25.5%) (thick line); shooting method (σ=24.5%) (thin line).

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Figure 6

Frequency response curve of the phase φ defined by Eq. 24. Multiple scales method (σ=25.5%) (thick line); shooting method (σ=24.5%) (thin line).

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Figure 7

Magnitudes of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=26.5%): stable responses (thick line); unstable responses (thin line); experimental results (σ=29.5%) (square).

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Figure 8

Phases of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=26.5%): stable responses (thick line); unstable responses (thin line); experimental results (σ=29.5%) (square).

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Figure 9

Magnitudes of the second harmonic component H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=25%): stable responses (thick line); unstable responses (thin line).

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Figure 10

Phases of the second harmonic components H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=25%): stable responses (thick line); unstable responses (thin line).

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Figure 11

The various regions in parameter space (ϖ,σ) for the existence of the steady state responses (TB) indicates transcritical bifurcation

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Figure 12

Time history of the dimensionless nonlinear elastic force transmitted through the contact at ϖ=0.484: (a) experimental result (σ=28.5%); and (b) theoretical result (σ=24.5%) obtained by the central difference method. Dashed line indicates zero force.

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Figure 13

Time history of the dimensionless nonlinear elastic force transmitted through the contact at ϖ=0.463: (a) experimental result (σ=29.5%); (b) theoretical result (σ=26.5%) obtained by the central difference method. Dashed line indicates zero force.

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