Reciprocity in Elastodynamics

Achenbach, Jan Drewes

doi:10.1017/cbo9780511550485

Cited by 139 publications

(70 citation statements)

References 48 publications

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“…(18) to (21)], who also considered propagation through layered anisotropic dielectric media. Note that the identity (7) 1 for the reflection coefficient is expected based on reciprocity [15]. Equation (5a) implies |T | = 1 when the impedances match,…”

Section: Acoustic Transmission Through a Slab With Anisotropic Inertiamentioning

confidence: 99%

Enhanced acoustic transmission through a slanted grating

Norris

2015

Comptes Rendus. Mécanique

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It is known that an acoustic wave incident on an infinite array of aligned rectangular blocks of a different acoustic material exhibits total transmission if certain conditions are met [1] which relate the unique "intromission" angle of incidence with geometric and material properties of the slab. This extraordinary acoustic transmission phenomenon holds for any slab thickness, making it analogous to a Brewster effect in optics, and is independent of frequency as long as the slab microstructure is sub-wavelength in the length-wise direction. Here we show that the enhanced transmission effect is obtained in a slab with grating elements oriented obliquely to the slab normal. The dependence of the intromission angle θ i is given explicitly in terms of the orientation angle. Total transmission is achieved at incidence angles ±θ i , with a relative phase shift between the transmitted amplitudes of the +θ i and −θ i cases. These effects are shown to follow from explicit formulas for the transmission coefficient. In the case of grating elements that are rigid the results have direct physical interpretation. The analytical findings are illustrated with full wave simulations.

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Section: Acoustic Transmission Through a Slab With Anisotropic Inertiamentioning

confidence: 99%

Enhanced acoustic transmission through a slanted grating

Norris

2015

Comptes Rendus. Mécanique

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“…[13,16]), however, a more compact and efficient formulation for the actual evaluation of T(z; S, T ) can be set up using an adjoint solution and is adopted here. The adjoint formulation stems from treating the integral in the left-hand side of (6) as one of the terms arising in the reciprocity identity linking two elastodynamic states [2,55], in which one state is the scattered field v a,z while the other is, like in [13,16], chosen as the adjoint statê u governed by the following IBVP…”

Section: Preliminariesmentioning

confidence: 99%

“…":") sign under the integral in (8). Now, for any generic bounded domain O and pair of elastodynamic states u i (i = 1, 2) satisfying Lu i = 0 and initial-rest conditions u i (ξ, 0) =u i (ξ, 0) = 0 in O, the following reciprocity identity holds [2,55]:…”

Section: Preliminariesmentioning

confidence: 99%

“…In this section, numerical experiments on 3-D configurations are presented to evaluate the efficiency of the topological derivative indicator for crack detection, based on the least-squares cost function defined by (2) and (3), using synthetic transient dynamical measurements. In contrast with the somewhat involved analysis required to arrive at the correct formulation (26a) of the TD field, subsequent numerical implementations require only standard computational engineering methods.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Qualitative identification of cracks using 3D transient elastodynamic topological derivative: Formulation and FE implementation

Bellis

Bonnet

2013

Computer Methods in Applied Mechanics and Engineering

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To cite this version:Cédric Bellis, Marc Bonnet. Abstract A time-domain topological derivative (TD) approach is developed for transient elasticwave imaging of buried cracks. The TD, which quantifies the sensitivity of the misfit cost functional to the creation at a specified location of an infinitesimal trial crack, is expressed in terms of the time convolution of the free field and an adjoint field as a function of that specified location and of the trial crack shape. Following previous studies on cavity identification in similar conditions, the TD field is here considered as a natural and computationally efficient approach for defining a crack location indicator function. This study emphasizes the implementation and exploitation of TD fields using the standard displacement-based FEM, a straightforward exploitation of the relevant sensitivity formulation established here. Results on several numerical experiments on 3D elastodynamic and acoustic configurations are reported and discussed, allowing to assess and highlight many features of the proposed TD-based fast qualitative crack identification, including its ability to identify multiple cracks and its robustness against data noise.

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“…Using the well known dynamical reciprocity identity [1] betweenũ ε andû and the boundary conditions in problems (3) and (5) one obtains…”

Section: Time Domain Formulation Via Adjoint Field Approachmentioning

confidence: 99%

Crack identification by 3D time-domain elastic or acoustic topological sensitivity

Bellis

Bonnet

2009

Comptes Rendus. Mécanique

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To cite this version:Cédric Bellis, Marc Bonnet.Crack identification by 3D time-domain elastic or acoustic topological sensitivity. Comptes Rendus Mécanique, Elsevier Masson, 2009Masson, , 337, pp.124-130. <10.1016Masson, /j.crme.2009 Crack identification by 3D time-domain elastic or acoustic topological sensitivity AbstractThe topological sensitivity analysis, based on the asymptotic behaviour of a cost functional associated with the creation of a small trial flaw in a defect-free solid, provides a computationally-fast, non-iterative approach for identifying flaws embedded in solids. This concept is here considered for crack identification using time-dependent measurements on the external boundary. The topological derivative of a cost function under the nucleation of a crack of infinitesimal size is established, in the framework of time-domain elasticity or acoustics. Introduction Consider an finite elastic body Ω ⋆ Γ ⊂ R 3 , externally bounded by the piecewise-smooth closed surface S, characterized by its shear modulus µ, Poisson's ratio ν and mass density ρ, and containing an internal crack idealized by the smooth open surface Γ ⋆ and with traction-free faces Γ ⋆± . Let Ω denote the crack-free solid such that Ω ⋆ Γ = Ω\Γ ⋆ . This Note is concerned with the identification of the crack Γ ⋆ from available measured displacement u obs on a measurement surface S obs ⊂ S resulting from the excitation of Ω ⋆ Γ by known applied timedependent tractions over the boundary S. The misfit between a trial cracked domain Ω Γ = Ω\Γ and the correct crack configuration Ω ⋆ Γ is expressed by means of a cost functional J of the form

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Reciprocity in Elastodynamics

Cited by 139 publications

References 48 publications

Enhanced acoustic transmission through a slanted grating

Enhanced acoustic transmission through a slanted grating

Qualitative identification of cracks using 3D transient elastodynamic topological derivative: Formulation and FE implementation

Crack identification by 3D time-domain elastic or acoustic topological sensitivity

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