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Experimental study and modeling of metamaterials for water surface waves

Abstract : This thesis concerns the study of metamaterials for water surface waves. The study is based on a laboratory experiment which makes it possible to measure the wave field precisely.In the first part, we demonstrate experimentally and numerically that metamaterials can be used to control the wave propagation and resonance properties of a closed cavity, including the cloaking of its eigenmodes. The anisotropic medium is designed using coordinate transformation theory and the homogenization of a three-dimensional linear water wave problem. This medium consists of a set of vertical plates whose spacing is much lower than the wavelength. This structure imposes an anisotropic bathymetry which influences the propagation of the waves differently according to their direction of propagation. Three different cavities manufactured by a 3D printer are tested and compared to the reference case with bathymetry without structuring. Fourier Transform Profilometry, as well as confocal displacement sensors, are used for measurements of water surface deformation resolved in time and space. Experimental data shows a remarkable ability of the metamaterial to influence the anisotropic propagation of waves on the water surface.The second part concerns the metamaterials submerged between two water layers for which a homogenized model is proposed, and the numerical solution by the modal method is provided. The anisotropic properties of such a structure are investigated experimentally using the same technique. An analysis based on the Bloch-Floquet formalism is performed to verify the dispersion relation of this medium predicted by the homogenization method.The main objective of the third part of this thesis is to experimentally study topologically protected edge states in a waveguide with periodic geometry in both linear and non-linear regimes. One of the representations of topological states, provided by the Su-Schrieffer-Heeger (SSH) model, is applied to describe the observed phenomena. A waveguide with periodic width is compared to the regular case of a rectangular reservoir with constant width. Confocal displacement sensors are used to measure the wave field very precisely. The experimental data is compared with the results of the 2D numerical simulations and the prediction of the SSH model. The results obtained show that this very simple configuration presents all the properties of the SSH model with excellent agreement.
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Submitted on : Friday, January 7, 2022 - 2:23:11 PM
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  • HAL Id : tel-03516863, version 1

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Adam Anglart. Experimental study and modeling of metamaterials for water surface waves. Mechanics [physics.med-ph]. Université Paris sciences et lettres, 2021. English. ⟨NNT : 2021UPSLS068⟩. ⟨tel-03516863⟩

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