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Nonlinear Localized Longitudinal Waves in a Metamaterial Designed as a “Mass-In-Mass” Chain

  • NONLINEAR ACOUSTICS
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Abstract

The article considers a mathematical model of an acoustic (mechanical) metamaterial, which is a chain of oscillators consisting of nonlinear elastic elements and masses, each of which contains an internal nonlinear oscillator. It is shown that, in the long-wavelength approximation, the resulting system of equations can be reduced to the Benjamin–Bon–Mahoney nonlinear evolutionary equation, in the framework of which interaction of three modulated quasi-harmonic waves (wave packets) is studied under the phase matching conditions. We investigate the formation of coupled three-frequency envelope solitons, i.e., wave packets that retain their amplitude–phase profiles as they propagate in the metamaterial due to the compensating effect of nonlinear effects. It is noted that in addition to solutions describing quasi-harmonic processes, the resulting evolutionary equation has an exact analytical solution in the form of a solitary stationary wave (soliton). Differences in the properties of this soliton and the classical Korteweg–de Vries soliton are revealed.

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Funding

The study was financed by the Russian Science Foundation (project no. 21-19-00813).

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Authors and Affiliations

  1. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Branch of Federal Research Center “Institute of Applied Physics of the RAS”, 603024, Nizhny Novgorod, Russia

    V. I. Erofeev, D. A. Kolesov & A. O. Malkhanov

Authors
  1. V. I. Erofeev
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  2. D. A. Kolesov
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  3. A. O. Malkhanov
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Correspondence to V. I. Erofeev.

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Erofeev, V.I., Kolesov, D.A. & Malkhanov, A.O. Nonlinear Localized Longitudinal Waves in a Metamaterial Designed as a “Mass-In-Mass” Chain. Acoust. Phys. 68, 423–426 (2022). https://doi.org/10.1134/S1063771022040030

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  • DOI: https://doi.org/10.1134/S1063771022040030

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