2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle

Chehade, Samar; Darmon, Michel; Lebeau, Gilles

doi:10.1016/j.jcp.2019.06.016

Cited by 5 publications

(4 citation statements)

References 35 publications

(60 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Observing (4.23), we note that at the second members we have that, in general, ψ bs (−m bi (γ , η)) contains discontinuous field components at the boundary u = 0, v < 0 of the angular region, while ψt (η, 0) (by definition 2. 16) is continuous at the boundary u > 0, v = 0. Similarly to what has been done in [1] for electromagnetic applications, we can repeat the procedure to obtain functional equations for regions 3 and 4 (figure 1).…”

Section: (B) From Region 1 To the Other Angular Regionsmentioning

confidence: 99%

“…An important aspect of this work is the use of recursive equations that provide analytical continuation (propagation of the solution) of the approximate spectral functions obtained by the numerical solution in a certain strip. New developments of this method are reported in [16], where double Fourier transforms are introduced to obtain the kernels of the singular integral equations. In [17], the method is extended to three-dimensional problems, however, the proposed functional equations in spectral domain are again written in terms of singular integral operators and not in an algebraic form.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

Daniele

Lombardi

2022

Proc. R. Soc. A.

View full text Add to dashboard Cite

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

show abstract

Section: (B) From Region 1 To the Other Angular Regionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

Daniele

Lombardi

2022

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…Note that when doing an asymptotic evaluation of the KA integral on a finite surface, the KA resulting leading terms describe the reflected waves, and the other terms describe diffracted waves by the surface edges which have the same nature (cylindrical or conical wave fronts) but not the same amplitude as those predicted by the geometrical theory of diffraction (GTD) [55,60]. The main advantage of the Kirchhoff approximation is to provide finite results for the scattered field in the whole space, contrary to GTD [61][62][63][64][65]. One of the main inconveniences of the Kirchhoff approximation (KA) is its incorrect quantitative prediction of edges diffraction, since the approximation of the surface field by the geometrical field is invalid near the edges.…”

Section: Theory and Historymentioning

confidence: 99%

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

Darmon

Dorval

Baqué³

2020

Applied Sciences

Self Cite

View full text Add to dashboard Cite

This paper proposes a brief review of acoustic wave scattering models from rough surfaces. This review is intended to provide an up-to-date survey of the analytical approximate or semi-analytical methods that are encountered in acoustic scattering from random rough surfaces. Thus, this review focuses only on the scattering of acoustic waves and does not deal with the transmission through a rough interface of waves within a solid material. The main used approximations are classified here into two types: the two historical approximations (Kirchhoff approximation and the perturbation theory) and some sound propagation models more suitable for grazing observation angles on rough surfaces, such as the small slope approximation, the integral equation method and the parabolic equation. The use of the existing approximations in the scientific literature and their validity are highlighted. Rough surfaces with Gaussian height distribution are usually considered in the models hypotheses. Rather few comparisons between models and measurements have been found in the literature. Some new criteria have been recently determined for the validity of the Kirchhoff approximation, which is one of the most used models, owing to its implementation simplicity.

show abstract

“…GTD is preferred to KA for simulating scattering by crack edges (notably for TOFD configurations [8,9]) but fails in the near-incident and specular reflection directions (shadow boundaries). A GTD solution has also recently been proposed for wedge scattering [10][11][12]. Several system models based on KA [3] or GTD [13,14] were conceived first for 2D configurations and then developed in 3D for KA [1,5] and for GTD [15], then using an incremental Huygens model [16].…”

Section: Introductionmentioning

confidence: 99%

An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks

2022

Self Cite

View full text Add to dashboard Cite

Ultrasonic Non-Destructive Testing (NDT) methods are broadly used for detection and characterization/imaging of cracks. Simulation is of great interest for designing such NDT methods. To model the ultrasonic 3D response of a crack, ultrasonic high frequency asymptotic (semi-analytical) models (such as the Physical Theory of Diffraction—PTD) are known to provide accurate predictions for most classical NDT configurations, and 3D numerical models have also emerged more recently. The aim of this paper is to carry out for the first time an experimental and theoretical comparison of 3D models for ultrasonic NDT of embedded cracks in 3D configurations. Semi-analytical models and a hybrid 3D FEM strategy—combining high-order spectral Finite Elements Method (FEM) for flaw scattering and an asymptotic ray model for beam propagation—have been compared. Both numerical validations and comparisons between simulation and experiments prove the effectiveness of PTD in numerous configurations but validate and demonstrate the improvement provided by the 3D hybrid code, notably for small flaws compared to the wavelength and for shear waves.

show abstract

2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle

Cited by 5 publications

References 35 publications

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances

An Experimental and Theoretical Comparison of 3D Models for Ultrasonic Non-Destructive Testing of Cracks: Part I, Embedded Cracks

Contact Info

Product

Resources

About