Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia

被引:0
作者
Angela Madeo
Manuel Collet
Marco Miniaci
Kévin Billon
Morvan Ouisse
Patrizio Neff
机构
[1] Université de Lyon,LGCIE SMS
[2] Institut Universitaire de France,ID, INSA
[3] Ecole Centrale de Lyon,Lyon
[4] Université du Havre,IUF
[5] Université de Bourgogne Franche-Comté,LTDS UMR
[6] Universitat Duisburg-Essen,CNRS 5513
来源
Journal of Elasticity | 2018年 / 130卷
关键词
Microstructure; Metamaterials; Phononic crystals; Relaxed micromorphic model; Gradient micro-inertia; Free micro-inertia; Complete band-gaps; Fitting of the elastic coefficients; Inverse approach; 74A10; 74A30; 74A60; 74E15; 74M25; 74Q15;
D O I
暂无
中图分类号
学科分类号
摘要
In this paper the relaxed micromorphic continuum model with weighted free and gradient micro-inertia is used to describe the dynamical behavior of a real two-dimensional phononic crystal for a wide range of wavelengths. In particular, a periodic structure with specific micro-structural topology and mechanical properties, capable of opening a phononic band-gap, is chosen with the criterion of showing a low degree of anisotropy (the band-gap is almost independent of the direction of propagation of the traveling wave). A Bloch wave analysis is performed to obtain the dispersion curves and the corresponding vibrational modes of the periodic structure. A linear-elastic, isotropic, relaxed micromorphic model including both a free micro-inertia (related to free vibrations of the microstructures) and a gradient micro-inertia (related to the motions of the microstructure which are coupled to the macro-deformation of the unit cell) is introduced and particularized to the case of plane wave propagation. The parameters of the relaxed model, which are independent of frequency, are then calibrated on the dispersion curves of the phononic crystal showing an excellent agreement in terms of both dispersion curves and vibrational modes. Almost all the homogenized elastic parameters of the relaxed micromorphic model result to be determined. This opens the way to the design of morphologically complex meta-structures which make use of the chosen phononic material as the basic building block and which preserve its ability of “stopping” elastic wave propagation at the scale of the structure.
引用
收藏
页码:59 / 83
页数:24
相关论文
共 189 条
  • [1] Armenise M.N.(2010)Phononic and photonic band gap structures: Modelling and applications Phys. Proc. 3 357-364
  • [2] Campanella C.E.(2012)Long wavelength inner-resonance cut-off frequencies in elastic composite materials Int. J. Solids Struct. 49 3269-3281
  • [3] Ciminelli C.(2013)Elastic metamaterials with inertial locally resonant structures: Application to lensing and localization Phys. Rev. B 87 437-440
  • [4] Dell’Olio F.(2000)Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres Nature 405 303-320
  • [5] Passaro V.M.N.(2003)Homogenisation of periodic discrete medium: Application to dynamics of framed structures Comput. Geotech. 30 517-534
  • [6] Auriault J.L.(2011)Generalized inner bending continua for linear fiber reinforced materials Int. J. Solids Struct. 48 1212-1224
  • [7] Boutin C.(2010)Dynamics of structural interfaces: Filtering and focussing effects for elastic waves J. Mech. Phys. Solids 58 359-376
  • [8] Bigoni D.(2003)Connecting molecular dynamics to micromorphic theory. (I). Instantaneous and averaged mechanical variables Physica A 322 2085-2097
  • [9] Guenneau S.(2004)Atomistic viewpoint of the applicability of microcontinuum theories Int. J. Solids Struct. 41 2837-2848
  • [10] Movchan A.B.(2011)Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems Int. J. Solids Struct. 48 27717-143