Elena Fedorovna's work — «Dynamics of reduced Kosser media and gyrocontinums» (scientific specialty 1.1.8 Mechanics of deformable solids) — is devoted to the construction of models of continuums of complex structure with the properties of acoustic metamaterials including granular and composite media, gyroscopic and other materials with rotating degrees of freedom of particles.

The relevance of the research is due to the need to develop new materials with desired wave properties for solving vibration isolation problems, controlling acoustic wave fronts, and the importance of modeling the wave processes in modern complex-structured materials.

In the dissertation, using the fundamental laws of mechanics, the principle of material objectivity, tensor algebra and analysis, asymptotic methods and analysis of variance, a new approach was developed to the continual modeling of acoustic metamaterials of various nature as well as of granular, block, consolidated bulk media, composite media with rigid inclusions.

The concept of a reduced medium was introduced, i.e., a continuum with the properties of an acoustic metamaterial under certain conditions.

The influence of various parameters of such a continuum on the wave properties of a material was studied, and various models of reduced Kosser media for block, granular and composite media with inclusions taking into account nonlinearity, anisotropy and dissipation were proposed.

The problem of propagation of waves from concentrated harmonic sources was solved, the features of the Rayleigh wave and its stability in such an isotropic medium was investigated, and a new mechanism for its instability was found. A model of a reduced Kelvin medium with the properties of acoustic gyroscopic and magnetically elastic metamaterials was proposed. The analysis of variance of the listed models was carried out. The theoretical and practical significance of the work lies in the fact that within the framework of the theory of continuous media of complex structure, a new direction was proposed — the theory of reduced elastic and viscoelastic media, which opens up opportunities for the search and development of smart acoustic metamaterials.

Reduced Kosser media may be used to model various media with a disordered rotation structure (geomedia, media of block and granular structure, composites with inclusions, etc.) in rotational seismology. The results obtained within the framework of these models are promising from the point of view of seismic exploration and ultrasound studies of media with microstructure. Reduced gyro-continuums are applicable as models of acoustic materials with gyroscopic elements, which have been developed in recent years to control wave fronts.

The work was prepared and defended on December 13, 2023 at IPMash RAS. Congratulations to Elena Fedorovna Grekova! We wish her further success and scientific recognition!