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Dans le contexte de l’acoustique on a systématisé la dérivation de modèles nonlinéaires(l’équation de Kuznetsov, l’équation KZK et la NPE). On a estimé le temps pourlequel des solutions régulières de ces modèles restent proches des solutions des systèmes deNavier-Stokes/Euler compressibles isentropiques (en précisant leur plus faible régularité) etétabli les résultats analogues entre les solutions des équations de KZK, NPE et Westerveltpar rapport à la solution de l’équation de Kuznetsov. Pour ce faire, on a étudié l’équationde Kuznetsov en commençant par le problème de Cauchy dans les cas visqueux (stabilité,unicité et existence globale des solutions régulières) et non-visqueux (caractère bien poséavec les estimations optimales du temps d’existence maximale des solutions régulières) etégalement dans un demi espace avec des conditions au limites périodiques en temps oudans un espace périodique dans une direction. On a aussi obtenu l’existence et l’unicité dessolutions faibles pour l’équation des ondes fortement amortie et l’équation deWestervelt surla plus large classe de domaines aux bords irréguliers, ainsi que la convergence asymptotiquedes solutions de l’équation de Westervelt avec conditions de Robin sur les bords préfractalsapproximant un bord fractal de type mixture de Koch. / In the framework of acoustic we systematize the derivation of nonlinear models(the Kuznetsov equation, the KZK equation and the NPE). We estimate the time for whichthe regular solutions of these models stay close of the solutions of the compressible isentropicNavier-Stokes/Euler systems (pointing out their weakest regularity) and establish similarresults between the solutions of the KZK, NPE and Westervelt equations with respectto the solutions of the Kuznetsov equation. To do so, we study the Kuznetsov equationbeginning by the Cauchy problem in the viscous case (stability, gobal well posedness ofregular solutions) and inviscid case (well posedness with optimal estimations of the maximalexistence time for regular solutions) and also in the half space with time periodic boundaryconditions or in a periodic in one direction space. We also obtain the existence and unicityof weak solutions for the strongly damped wave equation and the Westervelt equation in thelargest class of domains with irregular boundaries, along with the asymptotic convergenceof the solutions of the Westervelt equation with Robin boundary conditions on prefractalboundaries approximating a Koch mixture as fractal boundary.

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No description available.

Nearfield Acoustical Holography (NAH) is an acoustic field visualization technique that can be used to reconstruct three-dimensional (3-D) acoustic fields by projecting two-dimensional (2-D) data measured on a hologram surface. However, linear NAH algorithms developed and improved by many researchers can result in significant reconstruction errors when they are applied to reconstruct 3-D acoustic fields that are radiated from a high-level noise source and include significant nonlinear components. Here, planar, nonlinear acoustical holography procedures are developed that can be used to reconstruct 3-D, nonlinear acoustic fields radiated from a high-level noise source based on 2-D acoustic pressure data measured on a hologram surface. The first nonlinear acoustic holography procedure is derived for reconstructing steady-state acoustic pressure fields by applying perturbation and renormalization methods to nonlinear, dissipative, pressure-based Westervelt Wave Equation (WWE). The nonlinear acoustic pressure fields radiated from a high-level pulsating sphere and an infinite-size, vibrating panel are used to validate this procedure. Although the WWE-based algorithm is successfully validated by those two numerical simulations, it still has several limitations: (1) Only the fundamental frequency and its second harmonic nonlinear components can be reconstructed; (2) the application of this algorithm is limited to mono-frequency source cases; (3) the effects of bent wave rays caused by transverse particle velocities are not included; (4) only acoustic pressure fields can be reconstructed. In order to address the limitations of the steady-state, WWE-based procedure, a transient, planar, nonlinear acoustic holography algorithm is developed that can be used to reconstruct 3-D nonlinear acoustic pressure and particle velocity fields. This procedure is based on Kuznetsov Wave Equation (KWE) that is directly solved by using temporal and spatial Fourier Transforms. When compared to the WWE-based procedure, the KWE-based procedure can be applied to multi-frequency source cases where each frequency component can contain both linear and nonlinear components. The effects of nonlinear bent wave rays can be also considered by using this algorithm. The KWE-based procedure is validated by conducting an experiment with a compression driver and four numerical simulations. The numerical and experimental results show that holographically-projected acoustic fields match well with directly-calculated and directly-measured fields.