Active Cloaking for Finite Clusters of Pins in Kirchhoff Plates
| Autor: | Ö. Selsil, Richard V. Craster, S. G. Haslinger, Natalia V. Movchan, J. O'Neill |
|---|---|
| Přispěvatelé: | Engineering & Physical Science Research Council (EPSRC) |
| Rok vydání: | 2017 |
| Předmět: |
HOMOGENIZATION
Field (physics) Mathematics Applied Cloaking Geometry Stopband System of linear equations pinned Kirchhoff plate 01 natural sciences 010305 fluids & plasmas FLEXURAL WAVES PLATONIC GRATING STACKS ELASTIC PLATES 0102 Applied Mathematics 0103 physical sciences 010306 general physics Dispersion (water waves) Physics Science & Technology Applied Mathematics scattering DIRAC CONES active cloaking CYLINDERS CRYSTALS Amplitude Physical Sciences Biharmonic equation THIN PLATES Multipole expansion Mathematics HIGH-FREQUENCY ASYMPTOTICS |
| Zdroj: | SIAM Journal on Applied Mathematics. 77:1115-1135 |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/16m1088909 |
| Popis: | This paper considers active cloaking of a square array of evenly spaced pins in a Kirchhoff plate in the presence of flexural waves. Active sources, modeled as ideal point sources, are represented by the nonsingular Green's function for the two-dimensional biharmonic operator and have an arbitrary complex amplitude. These sources are distributed exterior to the cluster, and their complex amplitudes are found by solving an algebraic system of equations. This procedure ensures that selected multipole orders of the scattered field are successfully annulled. For frequencies in the zero-frequency stop band, we find that a small number of active sources located on a grid is sufficient for cloaking. For higher frequencies, we achieve efficient cloaking with the active sources positioned on a circle surrounding the cluster. We demonstrate the cloaking efficiency with several numerical illustrations, considering key frequencies from band diagrams and dispersion surfaces for a Kirchhoff plate pinned in a doubly periodic fashion. |
| Databáze: | OpenAIRE |
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