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Research Papers

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

[+] Author and Article Information
S. N. J. Costa

Department of Statistics, Applied Mathematics, and Computation, State University of São Paulo (UNESP), Rio Claro, São Paulo 13506-900, Brazilsanzara@terra.com.br

J. M. Balthazar

Department of Statistics, Applied Mathematics, and Computation, State University of São Paulo (UNESP), Rio Claro, São Paulo 13506-900, Braziljmbaltha@rc.unesp.br

J. Comput. Nonlinear Dynam 4(3), 031005 (May 19, 2009) (6 pages) doi:10.1115/1.3124090 History: Received February 29, 2008; Revised December 30, 2008; Published May 19, 2009

The purpose of this work is to investigate the control of the oscillations and the suppression of vibrations in damped and coupled oscillators. In this sense, we look into the potential of using a nonlinear energy sink in combination with an optimal linear control for nonlinear system to suppress structure vibrations under an impact load. As a result, we obtain that the nonlinear energy pumping (a one-way passive and almost irreversible energy flow from a linear main system to a nonlinear attachment that acts as a nonlinear energy sink) can be enhanced with the help of appropriate active control. The numerical results show the effectiveness of the approach presented here.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A two-degree-of-freedom model

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Figure 2

Schematic of the control flow

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Figure 3

Displacement of the main system for m=0.25 and γ=0.05

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Figure 4

Displacement of the main system for m=0.25 and (a) γ=0.09 and (b) γ=0.3

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Figure 5

Percentage of dissipated initial energy of the system

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Figure 6

Linear oscillator displacement for m=0.1: (dashed line) system without coupling; (thin solid line) pumping; (thick solid line) combined effects: pumping and OAC

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Figure 7

Percentage of dissipated initial energy of the system (m=0.1; ẏ2=0.42): (thick solid line) combined OAC and energy pumping; (dashed line) only energy pumping

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Figure 8

Displacement of the linear oscillator for m=0.1: (a) ẏ2=1 and (b) ẏ2=0.89; (dashed line) uncoupled; (thin solid line) pumping occurrence; (thick solid line) active and passive control strategies combined

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