Kushnierov I. The effect of localization of elastic waves in periodically-heterogeneous composite materials with imperfections.

Object of the study: the processes of propagation and localization of elastic waves in periodically-heterogeneous composite materials. Aim of the work: a theoretical study of propagation and localization of elastic waves in periodically-heterogeneous composite materials; determining the solutions that predict the relations between the characteristics of the elastic waves on macro level and the properties of microstructure. Methodology: the Floquet-Bloch method, the method of Fourier series, the transfer matrix method, the finite elements method using ANSYS. Theoretical and applied results: a general mechanism of the spatial localization of elastic waves in periodically-heterogeneous structures with imperfections is investigated; the dispersion curves, the phononic bandgaps and the attenuation coefficients for mass chains, for layered and fibrous composite materials are derived; the relations between the characteristics of elastic waves and the properties of the microstructure of composite materials are determined; the numerical simulations of the propagation of elastic waves in layered composite materials are performed using ANSYS; the effective elastic properties of fibrous composite materials are evaluated by the finite elements method. Novelty: the new analytical and numerical solutions describing propagation and localization of elastic waves in periodically-heterogeneous composite materials are proposed; the obtained results allow us to establish the links between the internal structure of the materials and the characteristics of waves on macro level. Implementation: the results of the study are used in the teaching process at the State Higher Educational Institution “Prydniprovska State Academy of Civil Engineering and Architecture”, namely, they are used in the lecture course “Numerical methods in engineering problems” for M.Sc. students at the Faculty of Civil Engineering. The scope of the practical applications: air, space and ship engineering, civil and mechanical engineering, structural health monitoring.