Nonlinear one-dimensional guided wedge waves

Lomonosov, Alexey M.; Pupyrev, Pavel D.; Hess, Peter; Mayer, Andreas

doi:10.1103/physrevb.92.014112

Cited by 10 publications

(4 citation statements)

References 20 publications

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“…It is worth noting that the study of strongly nonlinear elastic waves propagating in a wedge-shaped waveguide and known as wedge waves is longstanding challenge [14][15][16][17][18][19]. After the theoretical prediction of wedge waves subsequent experiments confirmed presence of nonlinearities induced by the laser-based pump-probe excitations [20][21][22].…”

Section: Introductionmentioning

confidence: 93%

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Possible realization of a phononic tsunami in a wedge-shaped sample

et al. 2021

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Exploiting the theory of solitons in a nonlinear elastic medium we predict a phenomenon called a phononic tsunami, which is characterized by the dramatic increase of the local amplitude of phonon modes. To elucidate the possible experimental detection of this phenomenon we propose to use a wedge-shaped sample in which a sharp edge serves for the emulation of the shoaling effect and such a local enhancement can be observed. Together with eigenfrequencies of transverse and longitudinal phonon modes of a system we find the characteristic dispersion relations that can be considered as a hallmark of a phononic tsunami. We justify our predictions by means of analytical calculations and numerical simulations showing a possible realization of this nonlinear effect in such a geometry. Our results provide the framework for the implementation of kind experiments aimed at realizing and investigating a phononic tsunami phenomenon in relevant materials.

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Section: Introductionmentioning

confidence: 93%

“…where ω and k are included in Eqs. ( 21) and (22). It is interesting to note that, due to the presence of the hyperbolic tangent function, the dispersion relation given by Eq.…”

Section: Clamped Edgesmentioning

confidence: 99%

Possible realization of a phononic tsunami in a wedge-shaped sample

et al. 2021

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“…This conclusion is supported both by the color of the modes '1′ and '2′ in Figure 4a and the components of their elastic fields, as represented Figure 4b. It is well known that such wedge waves, which are confined at solid edges, exhibit a phase velocity below those of surface and bulk waves [26]. These modes exist because of the finite size of the nanoridge.…”

Section: Propagation Parallel To the 1d Phononic Nanoridgementioning

confidence: 99%

Propagation of Elastic Waves in a One-Dimensional High Aspect Ratio Nanoridge Phononic Crystal

et al. 2018

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We investigate the propagation of elastic waves in a one-dimensional (1D) phononic crystal constituted by high aspect ratio epoxy nanoridges that have been deposited at the surface of a glass substrate. With the help of the finite element method (FEM), we calculate the dispersion curves of the modes localized at the surface for propagation both parallel and perpendicular to the nanoridges. When the direction of the wave is parallel to the nanoridges, we find that the vibrational states coincide with the Lamb modes of an infinite plate that correspond to one nanoridge. When the direction of wave propagation is perpendicular to the 1D nanoridges, the localized modes inside the nanoridges give rise to flat branches in the band structure that interact with the surface Rayleigh mode, and possibly open narrow band gaps. Filling the nanoridge structure with a viscous liquid produces new modes that propagate along the 1D finite height multilayer array.

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“…In crystal lattices, the elastic nonlinearity stems from the interatomic forces in the neighborhood of the rest positions of the atoms, which allows the potential energy of the solid to be expanded in powers of the Green-Lagrange strain tensor [6] and consequently, stress is an analytic function of strain. The influence of the third-order terms in this expansion on the propagation of surface and, to a lesser extent of wedge acoustic waves, has been investigated in theory and experiment (see the recent review [4], and [7]).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear effects of micro-cracks on acoustic surface and wedge waves

Rjelka

Pupyrev

Koehler

et al. 2018

Low Temperature Physics

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Micro-cracks give rise to non-analytic behavior of the stress-strain relation. For the case of a homogeneous spatial distribution of aligned flat micro-cracks, the influence of this property of the stress-strain relation on harmonic generation is analyzed for Rayleigh waves and for acoustic wedge waves with the help of a simple micromechanical model adopted from the literature. For the efficiencies of harmonic generation of these guided waves, explicit expressions are derived in terms of the corresponding linear wave fields. The initial growth rates of the second harmonic, i.e., the acoustic nonlinearity parameter, has been evaluated numerically for steel as matrix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for microcrack distributions with random orientation, using a model expression for the strain energy in terms of strain invariants known in a geophysical context.

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Nonlinear one-dimensional guided wedge waves

Cited by 10 publications

References 20 publications

Possible realization of a phononic tsunami in a wedge-shaped sample

Possible realization of a phononic tsunami in a wedge-shaped sample

Propagation of Elastic Waves in a One-Dimensional High Aspect Ratio Nanoridge Phononic Crystal

Nonlinear effects of micro-cracks on acoustic surface and wedge waves

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