On the Transfer of Energy Between Widely Spaced Modes

Malatkar, Pramod; Nayfeh, Ali H.

doi:10.2514/6.2003-1693

Cited by 20 publications

(24 citation statements)

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“…In Khusnutdinova and Pelinovsky (2003) the processes governing energy exchange between coupled KleinGordon oscillators were analyzed; the same weakly coupled system was studied in Maniadis, Kopidakis, and Aubry (2004), and it was shown that, under appropriate tuning, total energy transfer can be achieved for coupling above a critical threshold. In related work, localization of modes in a periodic chain with a local nonlinear disorder was analyzed (Cai, Chan, and Cheung (2000)); transfer of energy between widely spaced modes in harmonically forced beams was analytically and experimentally studied (Malatkar and Nayfeh (2003)); and a nonlinear dynamic absorber designed for a nonlinear primary was analyzed (Zhu, Zheng, and Fu (2004)). …”

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confidence: 99%

Irreversible Passive Energy Transfer in Coupled Oscillators with Essential Nonlinearity

Kerschen

Lee

Vakakis

et al. 2005

SIAM J. Appl. Math.

175

137

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Abstract. We study numerically and analytically the dynamics of passive energy transfer from a damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused by either fundamental or subharmonic resonance capture, and in some cases is initiated by nonlinear beat phenomena. It is shown that, due to the essential nonlinearity, the end attachment is capable of passively absorbing broadband energy at both high and low frequencies, acting, in essence, as a passive broadband boundary controller. Complicated transitions in the damped dynamics can be interpreted based on the topological structure and bifurcations of the periodic solutions of the underlying undamped system. Moreover, complex resonance capture cascades are numerically encountered when we increase the number of degrees of freedom of the system. The ungrounded essentially nonlinear end attachment discussed in this work can find application in numerous practical settings, including vibration and shock isolation of structures, seismic isolation, flutter suppression, and packaging. 1. Introduction. We study passive and irreversible energy transfer from a linear oscillator to an essentially nonlinear attachment, which, in essence, acts as a nonlinear energy sink (NES); such energy transfer we refer to as nonlinear energy pumping. In previous works (Vakakis and Gendelman (2001), Vakakis et al. (2003)) grounded and relatively heavy nonlinear attachments were considered, a feature that limits their attractiveness in practical applications. To eliminate these restrictions, an ungrounded and light nonlinear attachment is considered in this work, which, in addition, possesses the feature of modularity. As shown in Lee et al. (2005), even though the system considered has a simple configuration, it possesses a very complicated structure of undamped periodic orbits, which, in turn, give rise to a complicated

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mentioning

confidence: 99%

Irreversible Passive Energy Transfer in Coupled Oscillators with Essential Nonlinearity

Kerschen

Lee

Vakakis

et al. 2005

SIAM J. Appl. Math.

175

137

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“…In earlier studies by Nayfeh and coworkers [29][30][31][32][33][34], the modulation frequency was close to the first-mode natural frequency, and therefore large first-mode swaying was observed. Nayfeh developed a reduced-order analytical model by discretizing the integral partial-differential equation of motion.…”

Section: Introductionmentioning

confidence: 67%

“…These two frequencies are double values of the both s-eigen frequencies of the corresponding s-mode of the double belt system transversal vibration and are expressed by (33): Analog value of the potential energyẼ p(i) (η) of one belt (with out of the layer perennial energy interaction) is four frequency function η-coordinate in every s-eigen mode of the double belt system. These frequencies are double values of the both s-eigen frequencies of the corresponding s-mode (33) and values of the sum and of the difference of the two corresponding s-eineg mode of the double belt system transversal vibrations expressed by (34) and (35).…”

Section: Analysis Of the Analog Values Of The Kinetic And Potential Ementioning

confidence: 99%

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Energy transfer in the hybrid system dynamics (energy transfer in the axially moving double belt system)

Hedrih

2009

Arch Appl Mech

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First, as an introduction, using the author's published references, a short survey of an analytical study of the energy transfer between two coupled subsystems, as well as between a linear and nonlinear oscillators of a hybrid system, in the free and forced vibrations of a different type of inter connections between subsystems is presented. Second, as author's new research result, an analytical study of the energy transfer between two coupled like-string belts interconnected by light pure elastic layer in the axially moving sandwich double belt system, in the free vibrations is presented. On the basis of the obtained analytical expressions for the kinetic and potential energy of the belts and potential energy of the of light pure elastic distributed layer numerous conclusions are derived. In the pure linear elastic double belt system no transfer energy between different eigen modes of transversal vibrations of the axially moving double belt system, but in every from of the set of the infinite numbers eigen modes, there are transfer energy between belts. Each of the eigen modes of the free transversal vibrations are like two-frequency. The change of the potential energy of the booth belts is four frequency, and interaction part of the potential energy is one frequency in the each eigen mode. Changes of the kinetic energy of the both belts of the sandwich double axially moving bet system is two frequency like oscillatory regimes with two time multiplicities of the eineg frequencies of the corresponding eigen amplitude mode.

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“…This is observed in many experimental research results and also theoretical results [14,[19][20][21][22][23]. The interaction between amplitudes and phases of different modes in nonlinear systems with many degrees of freedom as well as in free and forced multi frequency regimes of deformable bodies with infinite number of vibration frequencies, is observed theoretically by averaging asymptotic method of Krilov-Bogoliyubov-Mitropolskiy [2,[15][16][17][18].…”

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confidence: 86%

Energy transfer in double plate system dynamics

Hedrih

2008

Acta Mech Sin

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The study of energy transfer between coupled subsystems in a hybrid system is very important for applications. This paper presents an analytical analysis of energy transfer between plates of a visco-elastically connected double-plate system in free transversal vibrations. The analytical analysis shows that the visco-elastic connection between plates is responsible for the appearance of two-frequency regime in the time function, which corresponds to one eigen amplitude function of one mode, and also that time functions of different vibration modes are uncoupled, but energy transfer between plates in one eigen mode appears. It was shown for each shape of vibrations. Series of the two Lyapunov exponents corresponding to the one eigen amplitude mode are expressed by using the energy of the corresponding eigen amplitude time component.Keywords Energy transfer between subsystems · Double plate system · Multifrequency transversal vibrations · Analytical solution · Rayleigh function of dissipation IntroductionPlates, beams and belts have been extensively used as structural elements in many industrial applications. Investigation of vibrations of plates dates back to the nineteenth century. The interest in the study of coupled systems [1-13] as newThe English text was polished

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On the Transfer of Energy Between Widely Spaced Modes

Cited by 20 publications

References 0 publications

Irreversible Passive Energy Transfer in Coupled Oscillators with Essential Nonlinearity

Irreversible Passive Energy Transfer in Coupled Oscillators with Essential Nonlinearity

Energy transfer in the hybrid system dynamics (energy transfer in the axially moving double belt system)

Energy transfer in double plate system dynamics

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