Vitesse d'une onde

Résumé

Une onde est une perturbation qui se déplace dans un milieu. Il est possible de lui associer deux vitesses d'onde, soit la vitesse de phase et la vitesse de groupe qui, parfois, ne sont pas égales :

Dans un milieu homogène, la propagation dans une direction donnée d'une onde monochromatique (ou sinusoïdale) se traduit par une translation de la sinusoïde à une vitesse appelée « vitesse de phase » ou « célérité ». Dans un milieu non dispersif, cette vitesse ne dépend pas de la fréquence. En superposant des ondes monochromatiques de diverses fréquences (ou pulsations), on obtient des ondes plus complexes (voir Analyse spectrale). Lorsque la vitesse de phase est indépendante de la fréquence, l'onde résultante subit aussi une translation globale de son profil, ceci sans déformation.
Dans un milieu dispersif ou lorsque les directions de propagation sont diverses (en dimension supérieure à 1), les composantes respectives se dispersent. Dans ce cas, il est souvent possible d’identifier de

Source officielle

https://fr.wikipedia.org/wiki/Vitesse_d'une_onde

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Cours associés (46)

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Elastodynamics of a Two-Dimensional Square Lattice With Entrained Fluid-Part I: Comparison With Biot's Theory

Vladimir Dorodnitsyn, Alessandro Spadoni

In the present paper, the performance of Biot's theory is investigated for wave propagation in cellular and porous solids with entrained fluid for configurations with well-known drained (no fluid) mechanical properties. Cellular solids differ from porous solids based on their relative density rho* < 0.3. The distinction is phenomenological and is based on the applicability of beam (or plate) theories to describe microstructural deformations. The wave propagation in a periodic square lattice is analyzed with a finite-element model, which explicitly considers fluid-structure interactions, structural deformations, and fluid-pressure variations. Bloch theorem is employed to enforce symmetry conditions of a representative volume element and obtain a relation between frequency and wavevector. It is found that the entrained fluid does not affect shear waves, beyond added-mass effects, so long as the wave spectrum is below the pores' natural frequency. One finds strong dispersion in cellular solids as a result of resonant scattering, in contrast to Bragg scattering dominant in porous media. Configurations with 0: 0001

Asme2014

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Elasto-Dynamic Behavior of a Two-Dimensional Square Lattice With Entrained Fluid II: Microstructural and Homogenized Models

Vladimir Dorodnitsyn, Alessandro Spadoni

This paper presents a detailed study of the pressure waves and effective mechanical properties of a closed-cell cellular solid with entrained fluid. Plane-harmonic-waves are analyzed in a periodic square with a finite-element model of a representative-volume element, which explicitly considers fluid-structure interactions, structural deformations, and the fluid dynamics of entrained fluid. The wall, cavity, and coupled-system resonance frequencies are identified as key parameters that describe the propagation characteristics. A tube-piston model based on computed microstructural deformations allows us to determine the effective stiffness tensor of an equivalent continuum at the macroscale. The analysis of dispersion surfaces indicates a single isotropic pressure mode for frequencies below resonance of the lattice walls, unlike Biot's theory which predicts two pressure modes. Shear modes are instead strongly anisotropic for all values of relative density rho* describing both cellular rho* < 0: 3 and porous solids rho* >= 0.3. The dependence of the pressure wave phase velocity on the relative density is analyzed for varying properties of the entrained fluid. Depending on the relative density and mass coupling of the solid and fluid phases, the microstructural deformations can be of three types: bending, through-the-thickness, and the combination of the two. For heavy and stiff entrained fluid, the bending regime is confined to extremely small values of relative density, whereas for light fluid such as a gas, deformations are of the bending-type for rho* < 0.1. Through-the-thickness deformations appear only for the heavy entrained fluid for large values of rho*.

Asme2014

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Complementary Metasurfaces for Guiding Electromagnetic Wave

Mohammad Sajjad Mirmoosa

Metasurfaces can be employed for designing waveguides that confine the electromagnetic energy while they are open structures. In this communication, we introduce a new type of such waveguides, formed by two penetrable metasurfaces having complementary isotropic surface impedances. We theoretically study the guided modes supported by the proposed structure and discuss the corresponding dispersion properties. We show the results for different scenarios in which the surface impedances possess nonresonant or resonant characteristics, and the distance between the two metasurfaces changes from large values to the extreme limit of zero. We also derive and describe the general condition for existence of two modes with orthogonal polarizations having the same phase velocity. In the particular case in which the metasurfaces are complementary and the distance between them is not small, we indicate that such phenomenon occurs within a broad frequency range. This property can be promising for applications in leaky-wave antennas and field focusing.

2021

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