New analytical approach to energy pumping problem in strongly nonhomogeneous 2dof systems

Manevitch, Leonid I.; Musienko, Andrey I.; Lamarque, Claude‐Henri

doi:10.1007/s11012-006-9021-y

Cited by 47 publications

(21 citation statements)

References 8 publications

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“…The dynamics of a system given by (1) using the Perturbation theory was presented in Manevitch, Musienko and Lamarque [12]. Here, we approached the same problem but of the control point of view.…”

Section: Problem Statementmentioning

confidence: 99%

“…Analytical, numerical and experimental results have been obtained considering energy pumping with a strong nonlinear coupling. For example, in Manevitch, Musienko and Lamarque [12], a new analytical approach to the problem of energy pumping in strongly nonhomogeneous nonlinear 2DOF systems with single anchor spring under condition of initial impact was presented. In that work, the authors have considered a resonance capture as the mechanism of energy pumping in the system under consideration.…”

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confidence: 99%

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Suppression of vibrations in strongly nonhomogeneous 2DOF systems

Costa

Balthazar

2009

Nonlinear Dyn

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In this work we analyze the effects of an optimal linear control for nonlinear systems under the vibrations of a strongly nonhomogeneous nonlinear twodegree-of-freedom system with single anchor spring under condition of initial impact. We compare the results with those obtained for (a) when using only a passive broadband boundary controller which, in essence, corresponds to a one-way passive and almost irreversible energy flow from a heavy or main system to a nonlinear energy sink (NES), and (b) when using the nonlinear energy sink in combination with the optimal linear control for nonlinear system.

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Section: Problem Statementmentioning

confidence: 99%

mentioning

confidence: 99%

Suppression of vibrations in strongly nonhomogeneous 2DOF systems

Costa

Balthazar

2009

Nonlinear Dyn

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“…The mass, damping, and stiffness matrices are derived applying Newton's second law. To solve the derived matrix system of equations, the authors propose and asymptotic expansion of the unknowns based on the approach proposed by Manevitch [17] assuming that the nonlinear coupling does not change the eigenmodes of the main system. The authors compare analytic results with the numerical ones, obtaining a good correlation between them which validates the proposed analytical method.…”

Section: Introductionmentioning

confidence: 99%

Experimental vibration analysis for a 3D scaled model of a three-floor steel structure

Castillo

Cruchaga

2012

Lat. Am. j. solids struct.

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In this paper we present an experimental study of a three dimensional physical model of a three-floor structure subjected to forced vibrations by imposing displacements in its support. The aim of this work is to analyze the behavior of the building when a dynamic vibration absorber (DVA) is acting. An analytic simplified analysis and a numerical study are developed to obtain the natural frequencies of the structure. Experiments are carried out in a vibrating table. The frequency range to be experimentally analyzed is determined by the first natural frequency of the structure for which the DVA damping effects are verified. The equipment capabilities, i.e. the frequencies, amplitudes and admissible load, limit the analyses. Nevertheless, satisfactory results are obtained for the study of the first mode of vibration. The effect of different amplitudes of the imposed support motion is also analyzed. In addition, the damping effect of the DVA device is evaluated upon varying its mass and its location in the structure. The characteristic curves in the frequency domain are obtained computing the Fast Fourier Transformation (FFT) of the acceleration history registered with piezoelectric accelerometers at different checkpoints for the cases analyzed.

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“…It has been proved that a system can be passively controlled by endowing nonlinear innate of coupled cubic systems, namely nonlinear energy sink (NES) to the main one [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There has been some attempts to consider the nonsmooth NES systems instead of cubic ones.…”

Section: Introductionmentioning

confidence: 99%