Non-stationary resonance dynamics of a nonlinear sonic vacuum with grounding supports

Koroleva, I. K.; Manevitch, Leonid I.; Vakakis, Alexander F.

doi:10.1016/j.jsv.2015.07.026

Cited by 15 publications

(6 citation statements)

References 17 publications

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“…The first problem relates to the properties of the sink itself in these conditions. This model has already been described several times [5][6][7]12,13].…”

Section: The Model and Equations Of Motionmentioning

confidence: 99%

“…It was shown recently [5][6][7] that a string with uniformly distributed discrete masses but without a preliminary stretching can demonstrate important regularities in its dynamical behaviour: the existence of well-defined nonlinear normal modes (NNMs) and a lot of possible resonances between them. The latter property which is strongly connected with providing the conditions of acoustic vacuum [5] allows one to consider such system as efficient energy sink for defence of different structural elements from intensive external excitations by means of almost irreversible targeted energy transfer (TET).…”

Section: Introductionmentioning

confidence: 99%

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Forced oscillations of the string under conditions of ‘sonic vacuum’

Sminrov

Manevitch

2018

Phil. Trans. R. Soc. A.

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We present the results of analytical study of the significant regularities which are inherent to forced nonlinear oscillations of a string with uniformly distributed discrete masses, without its preliminary stretching. It was found recently that a corresponding autonomous system admits a series of nonlinear normal modes with a lot of possible intermodal resonances and that similar synchronized solutions can exist in the presence of a periodic external field also. The paper is devoted to theoretical explanation of numerical data relating to one of possible scenarios of intermodal interaction which was numerically revealed earlier. This is unidirectional energy flow from unstable nonlinear normal mode to nonlinear normal modes with higher wavenumbers under the conditions of sonic vacuum. The mechanism of such a scenario has not yet been clarified contrary to alternative mechanisms consisting in almost simultaneous energy flow to all nonlinear normal modes with breaking the above-mentioned conditions of sonic vacuum. We begin with a description of single-mode manifolds and then show that consideration of arbitrary double mode manifolds is sufficient for solution of the problem. Because of this, the two-modal equations of motion can be reduced to a linear equation which describes a perturbation of initially excited nonlinear normal mode of the forced system in the conditions of sonic vacuum. We have found analytical representation (in the parametric space) of the thresholds for all possible energy transfers corresponding to unidirectional energy flow from unstable nonlinear normal modes. The analytical results are in a good agreement with previous numerical calculations.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

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“…The first problem relates to the properties of the sink itself in these conditions. This model has already been described several times [5][6][7]12,13].…”

Section: The Model and Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Forced oscillations of the string under conditions of ‘sonic vacuum’

Sminrov

Manevitch

2018

Phil. Trans. R. Soc. A.

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“…A natural question arises: how does the number of oscillators affect the efficiency of the sink. Our studies of the nonlinear dynamics of the sink [9,13] suggested that the efficiency of the sink would increase with the increase in the number of oscillators due to the appearance of multiple resonances. Therefore, after performing the first experimental study with a three-mass sink and making sure that the experimental results are in good agreement with the data of numerical simulation, we were able to compare the effects achieved with the use of a single-oscillator and three-oscillator sinks.…”

Section: Accounting For the Dissipation Influencesmentioning

confidence: 86%

Efficiency of a Three-Particle Energy Sink: Experimental Study and Numerical Simulation

Kevorkov¹,

Khamidullin²,

Koroleva³

et al. 2018

Nelin. Dinam.

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The results of an experimental and numerical investigation of the dynamics of a string with three uniformly distributed discrete masses are presented. This system can be used as a resonant energy sink for protecting structural elements from the effects of undesirable dynamic loads over a wide frequency range. Preliminary studies of the nonlinear dynamics of the system under consideration showed its high energy capacity. In this paper, we present the results of an experimental study in which a shaker's table mounted cantilever beam was being protected. As a result, the efficiency of the sink was confirmed, and data were also obtained to refine the mathematical model. It was shown that the experimental data obtained are in good agreement with the results of computer simulation.

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“…[25,26,29,[32][33][34]. For example [26] considers homogeneous chains of spherical, linearly elastic granules in contact, which in the long-wavelength approximation [35] generates the following nonlinear sonic vacuum, which is of infinite extent, non-smooth and caused by local interactions between granules:…”

Section: Targeted Energy Transfers In Nonlinear Acousticsmentioning

confidence: 99%

Passive nonlinear targeted energy transfer

Vakakis¹

2018

Phil. Trans. R. Soc. A.

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Nonlinearity in dynamics and acoustics may be viewed as scattering of energy across frequencies/wavenumbers. This is in contrast with linear systems when no such scattering exists. Motivated by irreversible large-to-small-scale energy transfers in turbulent flows, passive targeted energy transfers (TET) in mechanical and structural systems incorporating intentional strong nonlinearities are considered. Transient or permanent resonance captures are basic mechanisms for inducing TET in such systems, as well as nonlinear energy scattering across scales caused by strongly nonlinear resonance interactions. Certain theoretical concepts are reviewed, and some TET applications are discussed. Specifically, it is shown that the addition of strongly nonlinear local attachments in an otherwise linear dynamical system may induce energy scattering across scales and 'redistribution' of input energy from large to small scales in the linear modal space, in similarity to energy cascades that occur in turbulent flows. Such effects may be intentionally induced in the design stage and may lead to improved performance, e.g. it terms of vibration and shock isolation or energy harvesting. In addition, a simple mechanical analogue in the form of a nonlinear planar chain of particles composed of linear stiffness elements but exhibiting strong nonlinearity due to kinematic and geometric effects is discussed, exhibiting similar energy scattering across scales in its acoustics. These results demonstrate the efficacy of intentional utilization of strong nonlinearity in design to induce predictable and controlled intense multi-scale energy transfers in the dynamics and acoustics of a broad class of systems and structures, thus achieving performance objectives that would be not possible in classical linear settings.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

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Non-stationary resonance dynamics of a nonlinear sonic vacuum with grounding supports

Cited by 15 publications

References 17 publications

Forced oscillations of the string under conditions of ‘sonic vacuum’

Forced oscillations of the string under conditions of ‘sonic vacuum’

Efficiency of a Three-Particle Energy Sink: Experimental Study and Numerical Simulation

Passive nonlinear targeted energy transfer

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