Localisation near defects and filtering of flexural waves in structured plates
Source abstract
Abstract
The paper deals with localisation of flexural waves within gratings composed of either pinned points or rigid inclusions of finite radius in a structured plate. We study the filtering and resonant action of such systems. The effect of the finite size of inclusions on the dynamic localisation is analysed for the range of frequencies where only zeroth grating orders propagate. The structure of the resonant modes within gratings of inclusions is of special interest. In particular, we consider the circumstances under which such gratings can deliver for flexural waves a phenomenon similar to Electromagnetically Induced Transparency, where a resonant maximum of transmission is cut in two by a resonant minimum. We identify system designs which yield very high concentration of flexural fields within the interface that may lead to a further structural failure.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Ultrasonics and Acoustic Wave Propagation · Nonlinear Photonic Systems · Elasticity and Wave Propagation
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (24)
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1. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Reprint10.1063/1.3047921 ↗
2. Bertoldi K, Bigoni D, Drugan JW (2007a) Structural interfaces in linear elasticity. Part I: nonlocality and gradient approximations. J Mech Phys Solids 55:1–3410.1016/j.jmps.2006.06.004 ↗
3. Bertoldi K, Bigoni D, Drugan JW (2007b) Structural interfaces in linear elasticity. Part II: effective properties and neutrality. J Mech Phys Solids 55:35–6310.1016/j.jmps.2006.06.005 ↗
4. Bertoldi K, Bigoni D, Drugan JW (2007c) A discrete-fibers model for bridged cracks and reinforced elliptical voids. J Mech Phys Solids 55:1016–103510.1016/j.jmps.2006.10.007 ↗
5. Bigoni D, Gei M, Movchan AB (2008) Dynamics of a prestressed stiff layer on an elastic half space: filtering and band gap characteristics of periodic structural models derived from longwave asymptotics. J Mech Phys Solids 56:2494–252010.1016/j.jmps.2008.02.007 ↗
6. Bigoni D, Movchan AB (2002) Statics and dynamics of structural interfaces in elasticity. Int J Solids Struct 39:4843–486510.1016/S0020-7683(02)00416-X ↗
7. Born M, Wolf E (1959) Principles of optics. Pergamon Press, London
8. Botten LC, McPhedran RC, Lamarre JM (1985) Inductive grids in the resonant region: theory and experiment. Int J Infrared Millim Waves 6:511–57510.1007/BF01009671 ↗
9. Brun M, Guenneau S, Movchan AB, Bigoni D (2010) Dynamics of structural interfaces: filtering and focussing effects of elastic waves. J Mech Phys Solids 58(9):1212–122410.1016/j.jmps.2010.06.008 ↗
10. Evans DV, Porter R (2007) Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water. J Eng Maths 58:317–33710.1007/s10665-006-9128-0 ↗
11. Farhat M, Guenneau S, Enoch S, Movchan AB (2009) Cloaking bending waves propagating in thin elastic plates. Phys Rev B 79:03310210.1103/PhysRevB.79.033102 ↗
12. Farhat M, Guenneau S, Enoch S (2010) High directivity and confinement of flexural waves through ultra-refraction in thin perforated plates. Euro Phys Lett 91:5400310.1209/0295-5075/91/54003 ↗
13. Fleischhauer M, Imamoglu A, Marangos JP (2005) Electromagnetically induced transparency: optics in coherent media. Rev Mod Phys 77:633–67310.1103/RevModPhys.77.633 ↗
14. Gei M, Movchan AB, Bigoni D (2009) Band-gap shift and defect-induced annihilation in prestressed elastic structures. J Appl Phys 105:06350710.1063/1.3093694 ↗
15. Haslinger SG, Movchan NV, Movchan AB, McPhedran RC (2012) Transmission, trapping and filtering of waves in periodically constrained elastic plates. Proc R Soc A 468:76–9310.1098/rspa.2011.0318 ↗
16. Movchan AB, Movchan NV, McPhedran RC (2007) Bloch-Floquet bending waves in perforated thin plates. Proc R Soc A 463:2505–251810.1098/rspa.2007.1886 ↗
17. Movchan NV, McPhedran RC, Movchan AB, Poulton CG (2009) Wave scattering by platonic grating stacks. Proc R Soc A 465:3383–340010.1098/rspa.2009.0301 ↗
18. Movchan NV, McPhedran RC, Movchan AB (2011) Flexural waves in structured elastic plates: mindlin versus bi-harmonic models. Proc R Soc A 467:869–88010.1098/rspa.2010.0375 ↗
19. McPhedran RC, Movchan AB, Movchan NV (2009) Platonic crystals: bloch bands, neutrality and defects. Mech Mater 41:356–36310.1016/j.mechmat.2009.01.005 ↗
20. Pelton EL, Munk BA (1979) Scattering from periodic arrays of crossed dipoles. IEEE Trans AP-27, 323–33010.1109/TAP.1979.1142088 ↗
21. Poulton CG, McPhedran RC, Movchan NV, Movchan AB (2010) Convergence properties and flat bands in platonic crystal band structures using the multipole formulation. Waves Random Complex Media 20:702–71610.1080/17455030903203140 ↗
22. Stenger N, Wilhelm M, Wegener M (2012) Experiments on elastic cloaking in thin plates. Phys Rev Lett 108:01430110.1103/PhysRevLett.108.014301 ↗
23. Twersky V (1961) Elementary function representations of Schlömilch series. Arch Ration Mech Anal 8:323–33210.1007/BF00277447 ↗
24. Ulrich R, Tacke M (1973) Submillimeter wave-guiding on periodic metal structure. Appl Phys Lett 22:251–25310.1063/1.1654628 ↗