✦ LIBER ✦

Variational approach to scattering of plane elastic waves by diffraction gratings

✍ Scribed by Johannes Elschner; Guanghui Hu

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 286 KB
Volume: 33
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1305

No coin nor oath required. For personal study only.

✦ Synopsis

The scattering of a time-harmonic plane elastic wave by a two-dimensional periodic structure is studied. The grating profile is given by a Lipschitz curve on which the displacement vanishes. Using a variational formulation in a bounded periodic cell involving a nonlocal boundary operator, existence of solutions in quasiperiodic Sobolev spaces is investigated by establishing the Fredholmness of the operator generated by the corresponding sesquilinear form. Moreover, by a Rellich identity, uniqueness is proved under the assumption that the grating profile is given by a Lipschitz graph. The direct scattering problem for transmission gratings is also investigated. In this case, uniqueness is proved except for a discrete set of frequencies.

📜 SIMILAR VOLUMES

The scattering of plane elastic waves by

The scattering of plane elastic waves by a one-dimensional periodic surface

✍ T. Arens 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 158 KB 👁 2 views

The two-dimensional scattering problem for time-harmonic plane waves in an isotropic elastic medium and an effectively infinite periodic surface is considered. A radiation condition for quasi-periodic solutions similar to the condition utilized in the scattering of acoustic waves by one-dimensional

SOUND SCATTERING BY A HARD HALF-PLANE: E

SOUND SCATTERING BY A HARD HALF-PLANE: EXPERIMENTAL EVIDENCE OF THE EDGE-DIFFRACTED WAVE

✍ D. OUIS 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 150 KB

In this short note, some experimental results are presented on the di!raction of a spherical way by a hard half-plane. This study was conducted with the aim to give evidence to the existence of the edge-di!racted wave. The sound source used in this experimental study is a condenser microphone operat

Scattering of elastic waves by a plane c

Scattering of elastic waves by a plane crack of finite width in a transversely isotropic medium

✍ Carcione, J. M. 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 221 KB 👁 2 views

This work presents a numerical algorithm for solving crack scattering in a transversely isotropic medium whose symmetry axis is perpendicular to the crack surface. The crack is modelled as boundary discontinuities in the displacement u and the particle velocity v, of the stresses [ u# v], where the

Transient scattering of elastic waves by

Transient scattering of elastic waves by dipping layers of arbitrary shape. Part 2: Plane strain model

✍ Hossein Eshraghi; Marijan Dravinski 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 745 KB

Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion a

Scattering of plane wave by a 3D smooth

Scattering of plane wave by a 3D smooth convex impedance surface using physical theory of diffraction with transition currents

✍ Hirokazu Kobayashi; Kohei Hongo; Toshifumi Moriyama 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 404 KB

Scattering of plane harmonic SH, SV, P a

Scattering of plane harmonic SH, SV, P and rayleigh waves by non-axisymmetric three-dimensional canyons: A wave function expansion approach

✍ Hossein Eshraghi; Marijan Dravinski 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 805 KB