Abstract
In this paper, we analyze the effect of both deterministic and random perturbations of a regular multi-layered elastic structure on its stop band properties. The tool of choice is the transfer matrix method, which is both versatile and easy to implement. In both cases, we find that the stop-bands widen. We observe the appearance of very narrow pass-bands within the stop-bands, which can be observed in other instances in optics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Godin Y.A.: Propagation of longitudinal waves in a random binary rod. Waves Random Complex Media 16, 409–416 (2006)
Chen A.L., Wang Y.S.: Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals. Phys. B 392, 369–378 (2007)
Lekner J.: Light in periodically stratified media. J. Opt. Soc. Am. A 11, 2892–2899 (1994)
Felbacq D., Guizal B., Zolla F.: Limit analysis of the diffraction of a plane wave by a one-dimensional periodic medium. J. Math. Phys. 39, 4604–4607 (1998)
Hardy G.H., Wright E.M.: An Introduction to Number Theory, 5th edn. Oxford University Press, New York (1980)
Guenneau, S.: Homogenisation of quasi-crystals and analysis of modes in photonic crystal fibres. [Ph.D. Thesis], University of Aix-Marseille I (2001)
Zolla F., Felbacq D., Guizal B.: A remarkable diffractive property of photonic quasi-crystals. Opt. Commun. 148, 6–10 (1998)
Platts, S.: Mathematical modelling of wave propagation in disordered structures. [Ph.D. Thesis], University of Liverpool (2003)
Soven P.: Coherent-potential model of substitutional disordered alloys. Phys. Rev. 156, 809 (1967)
Papanicolaou, G.C., Varadhan, S.R.S.: Proceedings of a colloquium on random fields: rigorous results in statistical mechanics and quantum field theory. Coll. Mat. Soc. J. Bolyai, vol. 1. North-Holland/American Elsevier, Amsterdam (1979)
Barnes C., Pendry J.B.: Multiple scattering of waves in random media- a transfer matrix approach. Proc. Roy. Soc. Lond. A 435, 185–198 (1991)
Pendry J.B., Mackinnon A., Roberts P.J.: Universality classes and fluctuations in disordered systems. Proc. Roy. Soc. Lond. A 437, 67–83 (1992)
Pendry J.B.: Symmetry and waves in one-dimensional disordered systems. Adv. Phys. 43, 461–542 (1994)
Asatryan A.A., Botten L.C., Byrne M.A., Freilikher V.D., Gredeskul S.A., Shadrinov I.V., McPhedran R.C., Kivshar Y.S.: Suppression of Anderson localization in disordered metamaterials. Phys. Rev. Lett. 99(19), 193902 (2007)
Asatryan A.A., Robinson P.A., Botten L.C., McPhedran R.C., Nicorovici N.A., Sterke C.M.: Effects of disorder on wave propagation in two-dimensional photonic crystals. Phys. Rev. E 60(5), 6118–6127 (1999)
Stefanou N., Modinos A.: Scattering of electromagnetic waves by a disordered 2 dimensional array of spheres. J. Phys. Condens. Matter 5, 8859–8868 (1993)
Yannopapas V., Modinos A., Stefanou N.: Anderson localization of light in inverted opals. Phys. Rev. B 68, 193205 (2003)
Della Villa A., Enoch S., Tayeb G., Galdi V., Capolino F.: Bandgaps formation and multiple scattering in photonic quasicrystals with Penrose lattice. Phys. Rev. Lett. 94(18), 183903 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Guenneau, S., Movchan, A.B., Movchan, N.V. et al. Acoustic stop bands in almost-periodic and weakly randomized stratified media: perturbation analysis. Acta Mech Sin 24, 549–556 (2008). https://doi.org/10.1007/s10409-008-0180-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-008-0180-z