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Emergent subharmonic band gaps in nonlinear locally resonant metamaterials induced by autoparametric resonance

P. B. Silva1,*, M. J. Leamy2, M. G. D. Geers1, and V. G. Kouznetsova1

  • 1Eindhoven University of Technology P. O. Box 513, 5600 MB Eindhoven, The Netherlands
  • 2George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0405, USA

  • *pri.brands@gmail.com
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Phys. Rev. E 99, 063003 – Published 24 June, 2019

DOI: https://doi.org/10.1103/PhysRevE.99.063003

Abstract

With the aim of developing high-performance locally resonant metamaterials, the effect of nonlinear hyperelastic interactions between a rubberlike elastomeric local resonator and the host matrix is investigated. The results reveal a new emergent physical phenomenon not previously reported within the framework of elastoacoustic metamaterials: The appearance of a half subharmonic attenuation zone complementing the local resonance band gap around the fundamental frequency. Evidence of the emergent attenuation zone is provided by direct numerical simulations as well as semianalytical developments via the method of multiple scales. The analyses demonstrate that, in the considered nonlinear locally resonant metamaterial, the combined effects of autoparametric and local resonance induce saturation of the primary wave at certain conditions and, subsequently, promote energy exchange from a primary propagating wave to an evanescent subharmonic wave, giving rise to an additional attenuation zone. This opens new possibilities for the design of passive filtering devices for elastoacoustic waves.

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Corrections

9 July, 2019

Correction: The captions and images for Figures 4 and 5 were positioned improperly in the original layout and have been fixed.

Article Text

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Information

Phys. Rev. E 99, 063003– Published 24 June, 2019
  • Received 26 November 2018
  • Revised 29 May 2019
  • Corrected 9 July 2019
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