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TECHNICAL PAPERS

Towards the Design of an Optimal Energetic Sink in a Strongly Inhomogeneous Two-Degree-of-Freedom System

[+] Author and Article Information
L. I. Manevitch

N. N. Semenov Institute for Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, 119991 Moscow, Russia

E. Gourdon1

 Ecole Nationale des Travaux Publics de l’Etat, LGM, URA CNRS 1652, Rue Maurice Audin, F-69518 Vaulx en Velin Cedex, Francegourdon@entpe.fr

C. H. Lamarque

 Ecole Nationale des Travaux Publics de l’Etat, LGM, URA CNRS 1652, Rue Maurice Audin, F-69518 Vaulx en Velin Cedex, France

1

Corresponding author.

J. Appl. Mech 74(6), 1078-1086 (Aug 02, 2006) (9 pages) doi:10.1115/1.2711221 History: Received September 07, 2005; Revised August 02, 2006

Analytical, numerical, and experimental results of energy pumping in a strongly inhomogeneous two-degree-of-freedom system are to be presented in this study. The latter is based both on efficient analytical solution and comparative analysis for various types of energetic sinks. Considering the efficient pumping process as damped beating with strong energy transfer, it is shown that we can design the sinks with amplitude-phase variables which provide the most efficient result. In this study, the main types of energetic sinks are to be compared. Computer simulation has confirmed the analytical predictions which had been obtained. Experimental verification of the analytical prediction is considered for a particular type of sink.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 3

Responses with numerical integration of Eq. 1 with and without coupling.

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Figure 14

Considered system with 2 DOF

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Figure 1

Function H(t). Comparison between the numerical solution Eq. 12 and the analytical expression Eq. 13 for different orders of the Taylor series.

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Figure 2

Function H(t). Solid line depicts solution Eq. 13 taking into account the Taylor series up to the terms of the fifth order on τ1, inclusive. Dash line depicts the numerical solution of System 1.

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Figure 12

Experimental system

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Figure 13

Linear identification

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Figure 15

Comparison of experimental and numerical results

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Figure 16

Resonance capture phenomenon

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Figure 17

Comparison of experimental result with the numerical integration Eqs. 1

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Figure 4

Function H(t), Imagφ10(t), Reφ10(t), and Reφ20(t), compared with numerical integration of System 1

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Figure 5

Function H(t). Solid line depicts solution Eq. 13 taking into account the Taylor series up to the terms of the fifth order on τ1, inclusive. Dash line depicts the numerical solution of System 1.

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Figure 6

Comparison of function H(t): consideration of sign + or− in Eqs. 1

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Figure 7

Comparison of responses owing to numerical integration of 1: consideration of sign + or − in Eqs. 1

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Figure 8

Comparison of H(t) for different values of n

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Figure 9

Bifurcation diagrams: stationary solutions of Eq. 26

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Figure 10

Nonlinear beating with no damping

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Figure 11

Energy pumping activation with damping

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