Нелинейные волны деформации в волокнистом композиционном материале в случае неидеального контакта между компонентами

Abstract

RU: Получены аналитические решения, описывающие распространение периодических антиплоских нелинейных волн деформации в однонаправленном волокнистом композиционном материале в случае неидеального контакта между компонентами.

EN: Problem statement. Elastic waves propagating in micro-composite materials may be exposed to the effects of nonlinearity, dispersion and dissipation. Nonlinearity leads to localization of energy, higher harmonic generation and transfer of energy from low frequency to high frequency portion of the spectrum. Dispersion leads to energy dissipation. The steepness of the wave front is reduced, and thus, the effect becomes less pronounced nonlinearity. If the nonlinearity and dispersion act simultaneously, they compensate each other's influence. In this case, stationary periodic nonlinear waves can propagate. Strengthening of nonlinearity leads to the formation of localized bell–shaped waves (solitons) or impact waves (kinks). Such waves accumulate a lot of energy and are able to travel considerable distances, keeping constant shape and velocity.

Analyzing of the resent research. Nonlinear elastic waves in solids studied by many authors. Usually focused on homogeneous materials and structures, in which the effect of the dispersion part of geometrical factors. The impact of the dispersion on the propagation of nonlinear waves is studied less..

Research objective. This work investigates antiplanar nonlinear deformation waves propagating in a unidirectional fiber composite in the case of non-ideal contact between the components.

Conclusions. In this paper analytical solutions describing the propagation of nonlinear strain waves in a unidirectional fiber composite in the case of non–ideal contact between the components was obtained. Type of nonlinearity (soft or hard) fundamentally affects the nature of the decision. In the case of a soft non–linearity in the composite material can form localized strain wave impactor (kink), and a rigid wave nonlinearity localized deformations have a bell–shaped (solitons). Analysis of the numerical results obtained allows to estimate the range of applicability of various approximate theories that are used for modeling elastic waves in solids.