Abstract
The periodicity violation due to single or distributed cracks may change the wave reflection and transmission properties of periodically layered composites or one-dimensional phononic crystals . Numerical models for in-plane wave motion in layered phononic crystals with strip-like cracks are developed and the related wave propagation phenomena are investigated. For a prescribed incident wave field, the transfer matrix method is applied to calculate the reflected and the transmitted wave fields and to estimate the elastic wave band-gaps. The cracks are dealt with by using the integral approach, which represents the scattered wave field by a boundary integral containing the convolution of the Fourier-transform of the Green’s matrix of the corresponding layered structures and the crack-opening displacements. These unknown displacement jumps are calculated by applying the Bubnov-Galerkin scheme in conjunction with the boundary integral equation method . The typical wave characteristics describing the wave propagation phenomena related to the elastic wave scattering by cracks are analysed. Resonance wave scattering by interior or interface strip-like cracks (delaminations) is investigated, and the corresponding streamlines of the wave energy flow are demonstrated and discussed. Wave localization and focusing by cracks is also analysed and discussed.
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References
P.A. Deymier, Acoustic Metamaterials and Phononic Crystals (Springer-Verlag, Berlin Heidelberg, 2013)
M.I. Hussein, M.J. Leamy, M. Ruzzene, ASME Appl. Mech. Rev. 66(4), 040802 (2014)
Y. Wang, F. Li, Y.-S. Wang, K. Kishimoto, W. Huang, Acta. Mech. Sin. 25, 65 (2008)
M.V. Golub, Ch. Zhang, Wave Motion 54(2), 308 (2014)
M.V. Golub, Ch. Zhang, J. Acoust. Soc. Am. 137(1), 238 (2015)
M.V. Golub, Comput. Continuum Mech. 8(2), 136 (2015). (in Russian)
E. Glushkov, N. Glushkova, M.V. Golub, J. Moll, C.-P. Fritzen, Smart Mater. Struct. 21, 125001 (2012)
L.C. Parsons, G.T. Andrews, J. Appl. Phys. 111(12), 123521 (2012)
D. Schneider, F. Liaqat, H. El Boudouti, O. El Abouti, W. Tremel, H.-J. Butt, B. Djafari-Rouhani, G. Fytas, Phys. Rev. Lett. 111, 164301 (2013)
W. Thomson, J. Appl. Phys. 21, 89 (1950)
E.V. Glushkov, N.V. Glushkova, J. Comput. Acoust. 9(3), 889 (2001)
S.I. Fomenko, M.V. Golub, T.Q. Bui, Ch. Zhang, Y.-S. Wang, Int. J. Solids Struct. 51(13), 2491 (2014)
E.V. Glushkov, N.V. Glushkova, M.V. Golub, Ch. Zhang, Acoust. Phys. 55, 8 (2009)
E.V. Glushkov, N.V. Glushkova, A.A. Eremin, J. Acoust. Soc. Am. 129(12), 2923 (2011)
A. Bostrom, Appl. Mech. Rev. 56, 383 (2003)
A.P. Kiselev, J. Sov. Math. 19, 1372 (1982)
E.V. Glushkov, N.V. Glushkova, J. Acoust. Soc. Am. 102, 1356 (1997)
M. Farhat, S. Guenneau, S. Enoch, A.B. Movchan, G.G. Petursson, Appl. Phys. Lett. 96, 081909 (2010)
M. Dubois, M. Farhat, E. Bossy, S. Enoch, S. Guenneau, P. Sebbah, Appl. Phys. Lett. 103, 071915 (2013)
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Golub, M.V., Zhang, C. (2016). Numerical Simulation of Elastic Wave Propagation in Layered Phononic Crystals with Strip-Like Cracks: Resonance Scattering and Wave Localization. In: Parinov, I., Chang, SH., Topolov, V. (eds) Advanced Materials. Springer Proceedings in Physics, vol 175. Springer, Cham. https://doi.org/10.1007/978-3-319-26324-3_30
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DOI: https://doi.org/10.1007/978-3-319-26324-3_30
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