HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perflectly matched layer methodsKhac-Long Nguyen, Fabien Treyssede, Christophe Hazard To cite this version:Khac-Long Nguyen, Fabien Treyssede, Christophe Hazard. Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perflectly matched layer methods. AbstractAmong the numerous techniques of non destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes become necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.energy is confined into the core of waveguides without energy leakage into the surrounding medium allowing long inspection distances. Nevertheless, trapped modes do not always occur. For scalar open waveguides (characterized by a scalar field such as the acoustic pressure or the SH wave displacement), trapped modes exist only if the bulk velocity in the core is lower than in the surrounding medium [3]. In the elastic case, both compressional and shear bulk waves occur and, unless Stoneley waves are allowed on the interface between materials, no trapped modes are present when the shear velocity is faster in the core [4,5]. Unfortunately, such a configuration is often encountered in civil structures because the guiding structures are usually embedded in soft solid media such as concr...
Elastic guided waves have some potential for non-destructive inspection of civil engineering multi-wire steel cables. However, wave propagation inside such structures is not yet fully understood. This paper investigates multi-wire helical waveguides with special attention to the common seven-wire strand configuration (one straight core surrounded by one layer of six helical wires).
The goal of this paper is to theoretically investigate the propagation of elastic waves in helical waveguides. In the context of non-destructive evaluation for structural health monitoring, this study is motivated by the need for inspecting helical structures such as cables or springs. A numerical method is chosen based on a semi-analytical finite element technique. The proposed method relies on a non-orthogonal curvilinear coordinate system that is translationally invariant along the helix centreline, so that a Fourier transform is explicitly performed and the problem is reduced to two dimensions. Some useful expressions are also derived for the averaged energy and flux in order to directly compute the energy velocity. The convergence and accuracy of the proposed method are then assessed by comparing finite element results with reference solutions. A dispersion analysis inside a 7.5°helical wire, typically encountered in civil engineering cables, is realised including attenuation due to material damping. Some dispersion curves are finally presented for a wide range of lay angles and for several centreline radii. Significant differences with the infinite cylinder are observed.
Elastic guided waves are of interest for inspecting structures due to their ability to propagate over long distances. In numerous applications, the guiding structure is surrounded by a solid matrix that can be considered as unbounded in the transverse directions. The physics of waves in such an open waveguide significantly differs from a closed waveguide, i.e. for a bounded cross-section. Except for trapped modes, part of the energy is radiated in the surrounding medium, yielding attenuated modes along the axis called leaky modes. These leaky modes have often been considered in non destructive testing applications, which require waves of low attenuation in order to maximize the inspection distance. The main difficulty with numerical modeling of open waveguides lies in the unbounded nature of the geometry in the transverse direction. This difficulty is particularly severe due to the unusual behavior of leaky modes: while attenuating along the axis, such modes exponentially grow along the transverse direction. A simple numerical procedure consists in using absorbing layers of artificially growing viscoelasticity, but large layers may be required. The goal of this paper is to explore another approach for the computation of trapped and leaky modes in open waveguides. The approach combines the so-called semi-analytical finite element method and a perfectly matched layer technique. Such an approach has already been successfully applied in scalar acoustics and electromagnetism. It is extended here to open elastic waveguides, which raises specific difficulties. In this paper, two-dimensional stratified waveguides are considered. As it reveals a rich structure, the numerical eigenvalue spectrum is analyzed in a first step. This allows to clarify the spectral objects calculated with the method, including radiation modes, and their dependency on the perfectly matched layer parameters. In a second step, numerical dispersion curves of trapped and leaky modes are compared to analytical results.
The ambient temperature e ect may result in limitations of vibrationbased structural health monitoring (SHM) approaches for civil engineering structures. This paper addresses the issue of discriminating changes in modal parameters due to damages and changes in modal parameters due to temperature e ects. A n o n parametric damage detection algorithm is proposed, which only assumes that several datasets are recorded on the safe structure at di erent and unknown temperatures, and smoothes out the temperature e ect using an averaging operation. Key
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