title: Transient 3D elastodynamic field in an embedded multilayered anisotropic plate.
abstract: The aim of this paper is to study the ultrasonic response to a transient source that radiates ultrasonic waves in a 3D embedded multilayered anisotropic and dissipative plate. The source can be inside the plate or outside, in a fluid loading the plate for example. In the context of Non-Destructive Testing applied to composite materials, our goal is to create a robust algorithm to calculate ultrasonic field, irrespective of the source and receiver positions. The principle of the method described in this paper is well-established. This method is based on time analysis using the Laplace transform. In the present work, it has been customized for computing ultrasonic source interactions with multilayered dissipative anisotropic plates. The fields are transformed in the 2D Fourier wave-vector domain for the space variables related to the plate surface, and they are expressed in the partial-wave basis. Surprisingly, this method has been very little used in the ultrasonic community, while it is a useful tool which complements the much used technique based on generalized Lamb wave decomposition. By avoiding mode analysis - which can be problematic in some cases - exact numerical calculations (i.e., approximations by truncating infinite series that may be poorly convergent are not needed) can be made in a relatively short time for immersed plates and viscoelastic layers. Even for 3D cases, numerical costs are relatively low. Special attention is given to separate up- and down-going waves, which is a simple matter when using the Laplace transform. Numerical results show the effectiveness of this method. Three examples are presented here to investigate the quality of the model and the robustness of the algorithm: first, a comparison of experiment and simulation for a monolayer carbon-epoxy plate, where the diffracted field is due to a source located on the first free surface of the sample, for both dissipative and non-dissipative cases; second, the basic configuration of an aluminum plate immersed in water has been chosen to study wave propagation in ZGV (Zero Group Velocity) conditions; finally, a 2D plate consisting of 8 stacked carbon-epoxy layers immersed in water is treated, with a source located inside the plate, distributed in depth and extending over four layers.
authors.affiliation: Univ. Bordeaux, I(2)M-APy, UMR 5295, F-33400 Talence, France. Electronic address: pierric.mora@u-bordeaux.fr.
authors.forename: Pierric
authors.initials: P
authors.lastname: Mora
authors.affiliation: Univ. Bordeaux, I(2)M-APy, UMR 5295, F-33400 Talence, France; Arts et Metiers ParisTech, I(2)M-APy, UMR 5295, F-33400 Talence, France. Electronic address: eric.ducasse@u-bordeaux.fr.
authors.forename: Eric
authors.initials: E
authors.lastname: Ducasse
authors.affiliation: Univ. Bordeaux, I(2)M-APy, UMR 5295, F-33400 Talence, France; CNRS, I(2)M-APy, UMR 5295, F-33400 Talence, France. Electronic address: marc.deschamps@u-bordeaux.fr.
authors.forename: Marc
authors.initials: M
authors.lastname: Deschamps
keywords: Embedded multilayered plate; Integral transform domain; Numerical inverse Laplace transform; Partial-wave expansion; Transient ultrasonic response