An efficient method to compute the scattering of a guided wave by a localized defect, in an elastic waveguide of infinite extent and bounded cross section, is considered. It relies on the use of perfectly matched layers (PML) to reduce the problem to a bounded portion of the guide, allowing for a classical finite element discretization. The difficulty here comes from the existence of backward propagating modes, which are not correctly handled by the PML. We propose a simple strategy, based on finite-dimensional linear algebra arguments and using the knowledge of the modes, to recover a correct approximation to the solution with a low additional cost compared to the standard PML approach. Numerical experiments are presented in the two-dimensional case involving Rayleigh-Lamb modes.

International audienceWe consider an inverse scattering problem in a 3D homogeneous shallow ocean. Specifically, we describe a simple and efficient inverse method which can compute an approximation of the vertical projection of an immersed obstacle. This reconstruction is obtained from the far-field patterns generated by illuminating the obstacle with a single incident wave at a given fixed frequency. The technique is based on an implementation of the theory of the convex scattering support [S. Kusiak, J. Sylvester, The scattering support, Commun. Pure Appl. Math. (2003) 1525-1548]. A few examples are presented to show the feasibility of the method. © 2006 Elsevier B.V. All rights reserved

A finite element analysis of acoustic radiation in an infinite lined guide with mean flow is studied. In order to bound the domain, transparent boundary conditions are introduced by means of a Dirichlet to Neumann (DtN) operator based on a modal decomposition. This decomposition is easy to carry out in a hard-walled guide. With absorbant lining, many difficulties occur even without mean flow. Since the eigenvalue problem is no longer selfadjoint, acoustic modes are not orthogonal with respect to the L2-scalar product. However, an orthogonality relation exists which permits writing the modal decomposition. For a lined guide with uniform mean flow, modes are no longer orthogonal but a new scalar product allows us to define the DtN operator. We consider first the case of an infinite rectangular two-dimensional lined guide with uniform mean flow in order to present the methodology. Then, some extensions will be presented: non-uniform two-dimensional geometries by calculating potential mean flow, and cylindrical axisymmetric three-dimensional problems with uniform mean flow.

The potentiality of guided ultrasonic waves in Non Destructive Testing is currently investigated. Indeed, guided waves can allow a rapid inspection of large areas and of non accessible parts of particular structures like plates or pipes, compared to conventional techniques. This work concerns the numerical finite element computation, in the frequency domain, of the diffracted wave produced by a defect (crack, heterogeneity, discontinuity, local bend etc...) located in an infinite elastic waveguide. The computational domain is chosen as a portion of the waveguide, containing the perturbation, and our purpose is to build transparent conditions on its artificial boundaries by using modal representations. This cannot be achieved in a classical way, due to non standard properties of elastic modes. However, a biorthogonality relation is established which allows to derive a transparent condition relating hybrids displacement/stress vectors. An original mixed formulation is then implemented, whose unknowns are the displacement field in the bounded domain and the normal component of the normal stresses on the artificial boundaries. Numerical validations are presented in the two-dimensional and three-dimensional cases.