Abstract
The localization characteristics of the in-plane elastic waves in locally resonant aperiodic phononic crystals are examined in this study. In particular, the phononic crystals generated according to the Thue—Morse, Rudin—Shapiro and Period-Doubling sequences are theoretically investigated by using the extended transfer matrix method. For comparison, the binary and ternary locally resonant systems are considered, and their band structures are characterized by using the localization factors. Moreover, the influences of structural arrangement, material combination, incidence angle, number of components, length ratio, and random disorder on the band structures are also discussed. Some novel and interesting phenomena are observed and discussed.
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M.M. Sigalas, C.M. Soukoulis, Elastic wave propagation through disordered and/or absorptive layered systems, Phys. Rev. B 51 (1995) 13961.
M.M. Sigalas, E.N. Economou, Elastic and acoustic wave band structure, J. Sound Vib. 158 (1992) 377.
M.S. Kushwaha, Classical band structure of periodic elastic composites, Int. J. Mod. Phys. B9 (1996) 977.
Z. Liu, X.X. Zhang, Y.W. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Locally resonant sonic materials, Science 289 (2000) 1734.
S.X. Yang, J.H. Page, Z.Y. Liu, M.L. Cowan, C.T. Chan, P. Sheng, Focusing of sound in a 3D phononic crystal, Phys. Rev. Lett. 93 (2004) 024301.
S.J. Martinez-Sala R, J.V. Sanchez, V. Gomez, J. Llinares, F. Meseguer, Sound attenuation by sculpture, Nature 378 (1995) pp. 241–241.
Z.L. Hou, X.J. Fu, Y.Y. Liu, Calculational method to study the transmission properties of phononic crystals, Phys. Rev. B 70 (2004) 014304.
Y. Tanaka, Y. Tomoyasu, S. Tamura, Band structure of acoustic waves in phononic lattices: two-dimensional composites with large acoustic mismatch, Phys. Rev. B 62 (2000) 7378–7392.
M. Kafesaki, E.N. Economou, Multiple-scattering theory for three-dimensional periodic acoustic composites, Phys. Rev. B 60 (1999) 11993.
J.O. Vasseur, P.A. Deymier, B. Chenni, B. Djafari-Rouhani, L. Dobrzynski, D. Prevost, Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals, Phys. Rev. Lett. 86 (2001) 3012.
C. Goffaux, J. Sanchez-Dehesa, Two-dimensional phononic crystals studied using a variational method: application to lattices of locally resonant materials, Phys. Rev. B 67 (2003) 144301.
G. Wang, J.H. Wen, Y.Y. Liu, Lumped-mass method for the study of band structure in two-dimensional phononic crystals, Phys. Rev. B 69 (2004) 184302.
K. Bertoldi, L. Wang, Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures, Int. J. Solids Struct. 49 (2012) 2881–2885.
J.J. Chen, Q. Wang, X. Han, Lamb wave transmission through one-dimensional three-component Fibonacci composite plates, Mod. Phys. Lett. B 24 (2010) 161–167.
P.D. Sesion, E.I. Albuquerque, C. Chesman, V.N. Freire, Acoustic phonon transmission spectra in piezoelectric AlN/GaN Fibonacci phononic crystals, Eur. Phys. J. B 58 (2007) 379–387.
P.D.C. King, T.J. Cox, Acoustic band gaps in periodically and quasiperiodically modulated waveguides, J. Appl. Phys. 102 (2007) 014902.
H. Aynaou, E.H.EI. Boudouti, B Djafari-Rouhani, A Akjouj, V.R. Velasco, Propagation and localization of acoustic waves in Fibonacci phononic circuits, J. Phys. Condens. Matter. Phys. 17 (2005) 4245.
L.C. Parsons, G.T. Andrews, Observation of hypersonic phononic crystal effects in porous silicon superlattices, Appl. Phys. Lett. 95 (2009) 241909.
N.A. Gazi, G. Bernhard, Quasi-periodic Fibonacci and periodic one-dimensional hypersonic phononic crystals of porous silicon: experiment and simulation, J. Appl. Phys. 116 (2014) 094903.
Z.Z. Yan, C.Z. Zhang, Y.S. Wang, Wave propagation and localization in randomly disordered layered composites with local resonances, Wave Motion 47 (2010) 409–420.
Z.Z. Yan, C.Z. Zhang, Band structures and localization properties of aperiodic layered phononic crystals, Physica B 407 (2012) 1014–1019.
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Yan, Z., Wang, Y. & Zhang, C. A comparative study of wave localization in locally resonant Thue—Morse, Rudin—Shapiro and Period-Doubling aperiodic structures. Acta Mech. Solida Sin. 30, 271–284 (2017). https://doi.org/10.1016/j.camss.2017.03.007
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DOI: https://doi.org/10.1016/j.camss.2017.03.007