Approximate analysis of surface wave-structure interaction

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

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“…We also observe that the dispersion curves in Figure 4 look similar to those for seismic metasurfaces, see e.g. [9,11].…”

Section: Numerical Analysis Of the Dispersion Relationsupporting

confidence: 69%

Rayleigh-type waves on a coated elastic half-space with a clamped surface

Kaplunov

Приказчиков

Sultanova

2019

Phil. Trans. R. Soc. A.

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“…An array of flexural resonators attached to the surface of an elastic half-space is analysed using an explicit model for the Rayleigh wave. The paper generalises previous considerations using both full unimodal [23] and asymptotic solutions for an elastic half-space in the case of an array of compressional resonators [37].…”

Section: Discussionmentioning

confidence: 63%

An asymptotic hyperbolic–elliptic model for flexural-seismic metasurfaces

2019

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We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper we consider the effect of the flexural motion of the resonators, adapting a recently established asymptotic methodology that leads to an explicit scalar hyperbolic equation governing the propagation of Rayleigh-like waves. Compared with classical approaches, the asymptotic model yields a significantly simpler dispersion relation, with closed form solutions, shown to be accurate for surface wave-speeds close to that of the Rayleigh wave. Special attention is devoted to the effect of various junction conditions joining the beams to the elastic half-space which arise from considering flexural motion and are not present for the case of purely compressional resonators. Such effects are shown to provide significant and interesting features and, in particular, the choice of junction conditions dramatically changes the distribution and sizes of stop bands. Given that flexural vibrations in thin beams are excited more readily than compressional modes and the ability to model elastic surface waves using the scalar wave equation (i.e. waves on a membrane), the paper provides new pathways toward novel experimental set-ups for elastic metasurfaces. arXiv:1904.07690v2 [physics.class-ph]

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“…, = 1,2; ≠ and the asterisk denotes the Hilbert integral transform. In the forthcoming section, we adapt this asymptotic formulation (7) and (8) to the considered moving load problem.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The advantage of this approach is related to the representation of the surface wave field in terms of a single harmonic function, providing reduction of the vector problem of elastodynamics to a scalar formulation. Recent developments in this area include the incorporation of effects of anisotropy (Fu et al, 2020), a refined second-order model (Wootton et al, 2020), explicit formulations for seismic meta-surfaces in the form of an array of resonators attached to the surface (Ege et al, 2018;Wootton et al, 2019) and formulations for surface wave on a coated halfspace with non-classical boundary conditions (Kaplunov et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

Kudaibergenov

Приказчиков

2021

Acta Mechanica Et Automatica

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The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

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Approximate analysis of surface wave-structure interaction

Cited by 14 publications

References 11 publications

Rayleigh-type waves on a coated elastic half-space with a clamped surface

Rayleigh-type waves on a coated elastic half-space with a clamped surface

An asymptotic hyperbolic–elliptic model for flexural-seismic metasurfaces

Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

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