Emergence of non-stationary regimes in one- and two-dimensional models with internal rotators

Vorotnikov, K.; Kovaleva, Margarita; Starosvetsky, Yuli

doi:10.1098/rsta.2017.0134

Cited by 8 publications

(3 citation statements)

References 54 publications

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“…For example, although our parameter continuation in frequency revealed several families of solutions, there are undoubtedly -given the complexity of the studied system -several other ones (including possibly exotic ones) to discover. Other avenues for future work include the study of refined models -such as ones that account for nonlinear damping (or, more generally, a more elaborate form of damping [45][46][47]), rotational effects (which are often considered to be important [48,49]), and/or long-range interactions [37] -of our lattice system. Each of these aspects will add elements of complexity, but they also may lead to other types of interesting dynamics, such as the possibility of breather solutions with algebraically decaying tails of waves in space.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Chong,

Wang,

Marechal

et al. 2020

Preprint

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We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi-Pasta-Ulam-Tsingou lattice to model our experimental setup. Despite the idealized nature of the model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, driving along other directions leads to the creation of asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. When we vary the drive amplitude, we observe such behavior both in our experiments and in our simulations. We also demonstrate that solutions that appear to be time-quasi-periodic bifurcate from the branch of symmetric time-periodic NLMs.

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Section: Discussionmentioning

confidence: 99%

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Chong,

Wang,

Marechal

et al. 2020

Preprint

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“…In [190], proper orthogonal decomposition was applied to further explain the TET mechanisms. In addition, another series of research works has considered the concept of a transitionally coupled twodimensional model of locally resonant unit-cell incorporating an internal rotator for bidirectional and unidirectional energy channeling [257][258][259]. Accordingly, reversible and irreversible energy flows have been found to exist between longitudinal and lateral responses due to the coupled property of the NES which leads to efficient passive vibration control of the systems.…”

Section: Improvements Of VI Nessmentioning

confidence: 99%

A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types

2022

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Dynamical and structural systems are susceptible to sudden excitations and loadings such as wind gusts, blasts, earthquakes, and others which may cause destructive vibration amplitudes and lead to catastrophic impact on human lives and economy. Therefore, various vibration absorbers of linear and nonlinear coupling dynamics have been widely studied in plenty of publications where some have been applied in real-world practical applications. Firstly, the tuned-mass-damper (TMD), the first well-known linear vibration absorber that has been well-studied in the literature and applied with various structural and dynamical systems, is discussed. The linear vibration absorbers such as TMDs are widely used in real-life small- and large-scale structures due to their robust performance in vibration suppression of the low natural frequency structural modes. However, the TMD performs efficiently at narrowband frequency range where its performance is deteriorated by any changes in the frequency content in the structure and the TMD itself. Therefore, the targeted-energy-transfer mechanism which is found to be achieved by nonlinear energy sinks (NESs) has ignited the interest in passive nonlinear vibration suppression. Unlike TMDs, the NESs are dynamical vibration absorbers that achieve vibration suppression for wide range of frequency-energy levels. Given the very rapid growth in this field and the extensive research studies supporting the robustness of the NESs, this paper presents the different types of NESs and their applications with main emphasis on the rotary-based and impact-based NESs since they are of high impact in the literature due to their strong nonlinear dynamical behavior and robust targeted energy transfer.

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“…However, this work deals with more common systems, and the effects of global nonlinearity and sonic vacuum are obtained in appropriate asymptotic limits, due to the special choice of boundary conditions. The work of Starosvetsky [56] describes new possibilities for energy redirection and transfer that arise due to the use of internal rotating elements both in low-d.f. systems and in lattices.…”

Section: Contributionsmentioning

confidence: 99%

Introduction to a topical issue ‘nonlinear energy transfer in dynamical and acoustical Systems'

Gendelman

Vakakis

2018

Phil. Trans. R. Soc. A.

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This topical issue is devoted to recent developments in the broader field of energy transfer across scales in nonlinear dynamical and acoustical systems. Nonlinear energy transfers are common in Nature, with perhaps the most famous example being energy cascading from large to small length scales in turbulent flows. Yet nonlinearity has been traditionally perceived either as an unavoidable nuisance or as an unwelcome design restriction in engineering systems. Nowadays, however, this trend is reversing, with nonlinear phenomena being intensely studied in diverse disciplines. Furthermore, strong nonlinearity is now intentionally used and explored in a variety of mechanical and physical settings, such as granular media, acoustic metamaterials, nonlinear energy sinks, essentially nonlinear and nonlocal lattices, vibro-impact oscillators, vibration and shock isolation systems, nanotechnology, biomimetic systems, microelectronics, energy harvesters and in other applications. This topical issue is an attempt to document in a single volume some of these recent research developments, in order to establish a common basis and provide motivation and incentive for further development. The aim is to discuss and compare theoretical and experimental approaches pursued by research groups in different areas, and describe the state of the art of nonlinear energy transfer phenomena in an as broad as possible range of applications of current interest. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

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Emergence of non-stationary regimes in one- and two-dimensional models with internal rotators

Cited by 8 publications

References 54 publications

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

A review on nonlinear energy sinks: designs, analysis and applications of impact and rotary types

Introduction to a topical issue ‘nonlinear energy transfer in dynamical and acoustical Systems'

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