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A mathematical model is proposed that is a chain of oscillators consisting of nonlinear elastic elements and masses, each of which contains an internal nonlinear oscillator. Such a model describes a mass-to-mass acoustic metamaterial class. It is shown that the obtained system of equations can be reduced to the nonlinear evolutionary equation of Benjamin-Bona-Mahoni, showing that spatially localized nonlinear deformation waves (solitons) can form in the metamaterial under dynamic action on it.

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The work is devoted to a review of publications on the dynamics of deformable systems carrying moving loads, in the main areas of development and improvement of methods for calculating structures for the action of moving loads. The contribution to the formation and development of this scientific direction of domestic and foreign researchers is noted. A review of dissertation research on the wave dynamics of elastic systems interacting with moving loads is also given, including the analysis of doctoral and candidate dissertations.

We study the features of the propagation of a longitudinal wave in an acoustic (mechanical) metamaterial modeled as a one-dimensional chain containing the same masses connected by elastic elements (springs) having the same stiffness, each mass containing a series connection of another mass and a viscous element (damper). It is shown that the model under consideration allows us to describe the dispersion and frequency-dependent attenuation of a longitudinal wave, the nature of which substantially depends on the ratio of the external and internal masses of the metamaterial.