Oscillating vector solitary waves in soft laminates

Ziv, Ron; Gal, Shmuel

doi:10.1016/j.jmps.2020.104058

Cited by 4 publications

(4 citation statements)

References 62 publications

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“…Furthermore, Dai and Li [113] examined strongly nonlinear axisymmetric waves in a circular hyperelastic rod characterized by a compressible Mooney-Rivlin material model and observed the appearance of seven types of nonlinear waves, namely solitary waves of radial contraction and radial expansion, solitary shock waves of radial contraction and radial expansion, periodic waves and two types of periodic shock waves. Recently, the large-amplitude nonlinear elastic waves in soft periodic structures were investigated [114][115][116] and the experimental and numerical results demonstrated the existence of the vector solitary waves in these soft periodic structures. Moreover, the results revealed that the structural geometry and the initial deformation can be harnessed to tune the wave characteristics and control the selective generation of the solitary waves.…”

Section: Nonlinear Wavesmentioning

confidence: 99%

Vibrations and waves in soft dielectric elastomer structures

Zhao

Chen²,

Hu³

et al. 2023

International Journal of Mechanical Sciences

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Section: Nonlinear Wavesmentioning

confidence: 99%

Vibrations and waves in soft dielectric elastomer structures

Zhao

Chen²,

Hu³

et al. 2023

International Journal of Mechanical Sciences

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“…[6]). Nonlinearity can also be exploited to enable solitary wave propagation in soft metamaterials [7–9].…”

Section: Introductionmentioning

confidence: 99%

“…A special attribute of nonlinear systems is the tunability of their dynamic properties, which can overcome the inherent passivity of linear phononic crystals and metamaterials (a review of these effects is given by Bertoldi et al [6]). Nonlinearity can also be exploited to enable solitary wave propagation in soft metamaterials [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Wavenumber-space band clipping in nonlinear periodic structures

Gonella

2021

Proc. R. Soc. A.

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In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as an initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

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“…A special attribute of nonlinear systems is the tunability of their dynamic properties, which can overcome the inherent passivity of linear phononic crystals and metamaterials (a review of these effects is given by . Nonlinearity can also be exploited to enable solitary wave propagation in soft metamaterials (Raney et al, 2016;Deng et al, 2017;Ziv and Shmuel, 2020).…”

Section: Introductionmentioning

confidence: 99%

Wavenumber-space band clipping in nonlinear periodic structures

Jiao,

Gonella

2020

Preprint

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In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as a initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally-resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

show abstract

Oscillating vector solitary waves in soft laminates

Cited by 4 publications

References 62 publications

Vibrations and waves in soft dielectric elastomer structures

Vibrations and waves in soft dielectric elastomer structures

Wavenumber-space band clipping in nonlinear periodic structures

Wavenumber-space band clipping in nonlinear periodic structures

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