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Crystals 2016, 6(8), 86;

Second-Harmonic Generation in Membrane-Type Nonlinear Acoustic Metamaterials

LUNAM Université, Université du Maine, CNRS, LAUM UMR 6613, Av. O. Messiaen, Le Mans 72085, France
Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece
Author to whom correspondence should be addressed.
Academic Editors: Victor J. Sanchez-Morcillo, Vicent Romero-Garcia and Luis M. Garcia-Raffi
Received: 11 April 2016 / Revised: 21 July 2016 / Accepted: 25 July 2016 / Published: 29 July 2016
(This article belongs to the Special Issue Phononic Crystals)
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We study analytically and numerically the second-harmonic generation in a one-dimensional nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear dispersive wave equation. By applying the perturbation method to the latter, we derive the analytical expressions for the first- and second-harmonics, which are in excellent agreement with the numerical simulations of the nonlinear dynamical lattice model. Apart from the case of dispersionless nonlinear propagation and the Fubini solution, special attention is payed to the role of dispersion. In that regard, it is found that, once dispersion comes into play, second-harmonic beatings in space due to phase-mismatch can be identified. Our results provide many opportunities for the development of new periodic acoustic structures featuring both nonlinearity and dispersion. View Full-Text
Keywords: acoustic metamaterials; locally resonant materials; nonlinear acoustic propagation; higher harmonic generation acoustic metamaterials; locally resonant materials; nonlinear acoustic propagation; higher harmonic generation

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Zhang, J.; Romero-García, V.; Theocharis, G.; Richoux, O.; Achilleos, V.; Frantzeskakis, D.J. Second-Harmonic Generation in Membrane-Type Nonlinear Acoustic Metamaterials. Crystals 2016, 6, 86.

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