Abstract
A well-known mathematical model representing a chain of oscillators consisting of elastic elements and masses, each containing an internal oscillator and describing the class of acoustic metamaterials “mass-in-mass”, is generalized by taking into account the nonlinearity of the external and (or) internal elastic elements. As a result of analysis of the long-wavelength approximation of the obtained system, it is shown that spatially localized nonlinear deformation waves (solitons) can be formed in a metamaterial, under dynamic influence on it. The dependencies connecting the parameters of a localized wave are determined: amplitude, velocity and width with inertial and elastic characteristics of the metamaterial.
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Erofeev, V.I., Kolesov, D.A., Malkhanov, A.O. (2019). Nonlinear Localized Waves of Deformation in the Class of Metamaterials as Set as the Mass-in-mass Chain. In: Abali, B., Altenbach, H., dell'Isola, F., Eremeyev, V., Öchsner, A. (eds) New Achievements in Continuum Mechanics and Thermodynamics. Advanced Structured Materials, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-030-13307-8_8
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DOI: https://doi.org/10.1007/978-3-030-13307-8_8
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