On the dynamic behaviour of discrete metamaterials: From attenuation to energy localization

Joannopoulos, 2008, 446 2013, Acoustic Metamaterials and Phononic Crystals Laude, 2015, Phononic crystals Lu, 2009, Phononic crystals and acoustic metamaterials, Mater. Today, 12, 34, 10.1016/S1369-7021(09)70315-3 Kronig, 1931, Quantum mechanics of electrons in crystal lattices, Proc. R. Soc. London A, 130, 499, 10.1098/rspa.1931.0019 Goffaux, 2002, Evidence of Fano-like interference phenomena in locally resonant materials, Phys. Rev. Lett., 88, 225502/1, 10.1103/PhysRevLett.88.225502 Limonov, 2017, Fano resonances in photonics, Nat. Photonics, 11, 543, 10.1038/nphoton.2017.142 Milton, 2007, On modifications of Newton’s second law and linear continuum elastodynamics, Proc. R. Soc. A Math. Phys. Eng. Sci., 463, 855 Pham, 2017, Two scale homogenization of a row of locally resonant inclusions - the case of anti-plane shear waves, J. Mech. Phys. Solids, 106, 80, 10.1016/j.jmps.2017.05.001 Hu, 2005, Two-dimensional sonic crystals with Helmholtz resonators, Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys., 71, 1, 10.1103/PhysRevE.71.055601 Boutin, 2015, Theory and experiments on poro-acoustics with inner resonators, Wave Motion, 54, 76, 10.1016/j.wavemoti.2014.11.013 Pham, 2020, Scattering of acoustic waves by a nonlinear resonant bubbly screen, J. Fluid Mech., 906 Kaina, 2013, Composite media mixing bragg and local resonances for highly attenuating and broad bandgaps, Sci. Rep., 3, 3240, 10.1038/srep03240 Yuan, 2013, On the coupling of resonance and Bragg scattering effects in three-dimensional locally resonant sonic materials, Ultrasonics, 53, 1332, 10.1016/j.ultras.2013.03.019 Krushynska, 2017, Coupling local resonance with bragg band gaps in single-phase mechanical metamaterials, Extrem. Mech. Lett., 12, 30, 10.1016/j.eml.2016.10.004 Jensen, 2003, Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures, J. Sound Vib., 266, 1053, 10.1016/S0022-460X(02)01629-2 Brillouin, 1946, 248 Fallah, 2015, Wave propagation in two-dimensional anisotropic acoustic metamaterials of K4 topology, Wave Motion, 58, 101, 10.1016/j.wavemoti.2015.07.001 An, 2018, Elastic wave and vibration bandgaps in two-dimensional acoustic metamaterials with resonators and disorders, Wave Motion, 80, 69, 10.1016/j.wavemoti.2018.04.002 Comi, 2018, Wave propagation in cellular locally resonant metamaterials, Lat. Am. J. Solids Struct., 15, 10.1590/1679-78254327 Jaberzadeh, 2019, Wave propagation in an elastic metamaterial with anisotropic effective mass density, Wave Motion, 89, 131, 10.1016/j.wavemoti.2019.03.009 Chen, 2016, Dissipative elastic metamaterials for broadband wave mitigation at subwavelength scale, Compos. Struct., 136, 358, 10.1016/j.compstruct.2015.09.048 Kulkarni, 2016, Longitudinal elastic wave propagation characteristics of inertant acoustic metamaterials, J. Appl. Phys., 119 Frandsen, 2017, Modal interaction and higher harmonic generation in a weakly nonlinear, periodic mass–spring chain, Wave Motion, 68, 149, 10.1016/j.wavemoti.2016.09.002 Abbasi, 2020, Wave dispersion and dissipation performance of locally resonant acoustic metamaterials using an internal variable model, Wave Motion, 93, 10.1016/j.wavemoti.2019.102483 Yao, 2008, Experimental study on negative effective mass in a 1D mass–spring system, New J. Phys., 10, 10.1088/1367-2630/10/4/043020 Huang, 2009, On the negative effective mass density in acoustic metamaterials, Internat. J. Engrg. Sci., 47, 610, 10.1016/j.ijengsci.2008.12.007 Huang, 2009, Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density, New J. Phys., 11, 10.1088/1367-2630/11/1/013003 Auriault, 2012, Long wavelength inner-resonance cut-off frequencies in elastic composite materials, Int. J. Solids Struct., 49, 3269, 10.1016/j.ijsolstr.2012.07.002 Comi, 2020, Homogenization approach and Bloch-Floquet theory for band-gap prediction in 2D locally resonant metamaterials, J. Elasticity, 139, 61, 10.1007/s10659-019-09743-x Comi, 2019, Two scale homogenization in ternary locally resonant metamaterials, Mater. Phys. Mech., 44, 8 Parnell, 2013, Antiplane elastic wave cloaking using metamaterials, homogenization and hyperelasticity, Wave Motion, 50, 1140, 10.1016/j.wavemoti.2013.06.006 Mitchell, 2014, Metaconcrete: Designed aggregates to enhance dynamic performance, J. Mech. Phys. Solids, 65, 69, 10.1016/j.jmps.2014.01.003 Schittny, 2013, Experiments on transformation thermodynamics: Molding the flow of heat, Phys. Rev. Lett., 110, 10.1103/PhysRevLett.110.195901 Jung, 2019, Realisation of a locally resonant metamaterial on the automobile panel structure to reduce noise radiation, Mech. Syst. Signal Process., 122, 206, 10.1016/j.ymssp.2018.11.050 Montroll, 1955, Effect of defects on lattice vibrations, Phys. Rev., 100, 525, 10.1103/PhysRev.100.525 Maradudin, 1965, Some effects of point defects on the vibrations of crystal lattices, Rep. Progr. Phys., 28, 331, 10.1088/0034-4885/28/1/310 Sigalas, 1997, Elastic wave band gaps and defect states in two-dimensional composites, J. Acoust. Soc. Am., 101, 1256, 10.1121/1.418156 Sigalas, 1998, Defect states of acoustic waves in a two-dimensional lattice of solid cylinders, J. Appl. Phys., 84, 3026, 10.1063/1.368456 Wu, 2001, Point defect states in two-dimensional phononic crystals, Phys. Lett. Sect. A Gen. At. Solid State Phys., 292, 198 Wu, 2010, Wave propagation in a 2D sonic crystal with a Helmholtz resonant defect, J. Phys. D. Appl. Phys., 43, 10.1088/0022-3727/43/5/055401 Wu, 2009, Acoustic energy harvesting using resonant cavity of a sonic crystal, Appl. Phys. Lett., 95, 10.1063/1.3176019 Lv, 2013, Vibration energy harvesting using a phononic crystal with point defect states, Appl. Phys. Lett., 102, 2013, 10.1063/1.4788810 Lv, 2019, Highly localized and efficient energy harvesting in a phononic crystal beam: Defect placement and experimental validation, Crystals, 9, 10.3390/cryst9080391 Jo, 2020, Elastic wave localization and harvesting using double defect modes of a phononic crystal, J. Appl. Phys., 127, 10.1063/5.0003688 Jo, 2020, Designing a phononic crystal with a defect for energy localization and harvesting: Supercell size and defect location, Int. J. Mech. Sci., 179, 10.1016/j.ijmecsci.2020.105670 M. Moscatelli, C. Comi, J.-J. Marigo, Locally resonant materials for energy harvesting at small scale, in: Proc. XXIV AIMETA Conf. 2019, Rome, 2020, pp. 606–626. Moscatelli, 2020, Energy localization through locally resonant materials, Materials, 13, 3016, 10.3390/ma13133016 Jo, 2021, An analytical model of a phononic crystal with a piezoelectric defect for energy harvesting using an electroelastically coupled transfer matrix, Int. J. Mech. Sci., 193, 10.1016/j.ijmecsci.2020.106160 Terao, 2016, Wave propagation in acoustic metamaterial double-barrier structures, Phys. Status Solidi Appl. Mater. Sci., 213, 2773, 10.1002/pssa.201600156