Mode propagation in curved waveguides and scattering by inhomogeneities: Application to the elastodynamics of helical structures

Treyssède, Fabien

doi:10.1121/1.3559682

Cited by 22 publications

(27 citation statements)

References 50 publications

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“…Without PML (γ=1), this expression coincides with the results standardly found for closed waveguide problems [48,49]. With PMLs, M is complex and E tot is no longer real.…”

Section: Modal Filtering Of Radiation Modessupporting

confidence: 74%

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Treyssède¹,

Nguyen²,

Bonnet-Bendhia³

et al. 2014

Wave Motion

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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.

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“…Without PML (γ=1), this expression coincides with the results standardly found for closed waveguide problems [48,49]. With PMLs, M is complex and E tot is no longer real.…”

Section: Modal Filtering Of Radiation Modessupporting

confidence: 74%

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Treyssède¹,

Nguyen²,

Bonnet-Bendhia³

et al. 2014

Wave Motion

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“…This result is the same as for closed waveguides (without PML) [21,47]. In the presence of PML, the slight difference is that M is no longer real and the kinetic energy becomes complex.…”

Section: Kinetic Energysupporting

confidence: 70%

“…n is the unit vector normal to the cross section (in the z direction). The potential energy E p and the complex power flow S P·ndS can be post-processed from SAFE matrices thanks to the following formula [47], here modified for complex wavenumbers:…”

Section: Energy Velocitymentioning

confidence: 99%

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Nguyen¹,

Treyssède²,

Hazard

2015

Journal of Sound and Vibration

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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...

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“…The eigenforce concept has recently been used by the authors in Refs. [29,30] in the context of scattering of guided waves by inhomogeneities.…”

Section: Definition Of Eigenforcesmentioning

confidence: 99%

Numerical and analytical calculation of modal excitability for elastic wave generation in lossy waveguides

Treyssède¹,

Laguerre²

2013

The Journal of the Acoustical Society of America

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In the analysis of elastic waveguides, the excitability of a given mode is an important feature defined by the displacement-force ratio. Useful analytical expressions have been provided in the literature for modes with real wavenumbers (propagating modes in lossless waveguides). The central result of this paper consists in deriving a generalized expression for the modal excitability valid for modes with complex wavenumbers (lossy waveguides or non-propagating modes). The analysis starts from a semi-analytical finite element method and avoids solving the left eigenproblem. Analytical expressions of modal excitability are then deduced. It is shown that the fundamental orthogonality property to be used indeed corresponds to a form of Auld's real orthogonality relation, involving both positive- and negative-going modes. Finally, some results obtained from the generalized excitability are compared to the approximate lossless expression.

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Mode propagation in curved waveguides and scattering by inhomogeneities: Application to the elastodynamics of helical structures

Cited by 22 publications

References 50 publications

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Finite element computation of trapped and leaky elastic waves in open stratified waveguides

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Numerical and analytical calculation of modal excitability for elastic wave generation in lossy waveguides

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