Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Galán, José M.; Abascal, Ramón

doi:10.1121/1.1857525

Cited by 26 publications

(10 citation statements)

References 24 publications

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“…It can be concluded that a rough criterion of k s /h = 25 is thus quite acceptable, which may be not the case for k s /h = 10. Note that it coincides well with the criterion proposed for SAFE methods by Galan and Abascal [33,34] when using 3-node triangles.…”

Section: Convergence and Accuracysupporting

confidence: 65%

Elastic waves in helical waveguides

Treyssède

2008

Wave Motion

102

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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.

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Section: Convergence and Accuracysupporting

confidence: 65%

Elastic waves in helical waveguides

Treyssède

2008

Wave Motion

102

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“…The solution of the hybrid system directly yields the coefficients of scattered modes. In the literature, hybrid methods have already been proposed for elastic guided waves in two-dimensional straight waveguides (plates [32][33][34][35][36][37] and cylinders 38 ) as well as acoustic waves in ducts 39,40 for instance. A close relationship between hybrid and Dirichletto-Neumann approaches can be demonstrated, as done in Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Treyssède

2011

The Journal of the Acoustical Society of America

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This paper reports on an investigation into the propagation of guided modes in curved waveguides and their scattering by inhomogeneities. In a general framework, the existence of propagation modes traveling in curved waveguides is discussed. The concept of translational invariance, intuitively used for the analysis of straight waveguides, is highlighted for curvilinear coordinate systems. Provided that the cross-section shape and medium properties do not vary along the waveguide axis, it is shown that a sufficient condition for invariance is the independence on the axial coordinate of the metric tensor. Such a condition is indeed checked by helical coordinate systems. This study then focuses on the elastodynamics of helical waveguides. Given the difficulty in achieving analytical solutions, a purely numerical approach is chosen based on the so-called semi-analytical finite element method. This method allows the computation of eigenmodes propagating in infinite waveguides. For the investigation of modal scattering by inhomogeneities, a hybrid finite element method is developed for curved waveguides. The technique consists in applying modal expansions at cross-section boundaries of the finite element model, yielding transparent boundary conditions. The final part of this paper deals with scattering results obtained in free-end helical waveguides. Two validation tests are also performed.

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“…They used it to develop a mode decomposition technique for an elastodynamic field and semianalytically obtained the reflection coefficients for the oblique incidence problem. In addition, it is important to understand the interaction of Lamb modes with a plate edge which has been studied and reported quite extensively [9][10][11][12][13][14][15]. It has been shown that the incident wave, interacting with a free plate edge, gives rise to a system of reflected waves, consisting of propagating and non-propagating modes.…”

Section: Introductionmentioning

confidence: 99%

Separation of Lamb modes at a plate edge by using orthogonality relation

Ratassepp

Klauson²,

Chati³

et al. 2013

Estonian J. Eng.

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Lamb modes are widely used for non-destructive evaluation of plate-like structures and simple interpretation procedures for the analysis of the monitored structures are needed. In this study we apply the orthogonality relation based method for post-processing Finite Element (FE) predictions in order to separate Lamb modes at a plate edge. The reflected wave field from the free edge is a superposition of all the eigenmodes of an infinite plate. The eigenmode amplitudes of the reflected wave field are determined by applying the orthogonality-based method. Overlapping wavepackets of Lamb modes at a plate edge are simulated by using the FE model of the incident S 0 mode in a plate with a crack. Time-domain signals of propagating and non-propagating modes are extracted.

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Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Cited by 26 publications

References 24 publications

Elastic waves in helical waveguides

Elastic waves in helical waveguides

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

Separation of Lamb modes at a plate edge by using orthogonality relation

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