Макроскопическое нелинейное волновое уравнение для волокнистого композиционного материала в случае неидеального контакта между компонентами

Abstract

RU: Получено макроскопическое волновое уравнение, описывающее распространение нелинейных волн деформации в волокнистом композиционном материале в случае неидеального контакта между компонентами. Для этой цели развит асимптотический метод осреднения высшего порядка. Найдены эффективные упругие коэффициенты и выполнен анализ полученных численных результатов.

EN: Problem statement. Nonlinear strain wave play an important role in the mechanics of composites. Generation of localized waves accompanied by a significant increase in their amplitude. This may lead to areas of plasticity and development of micro cracks. Thus, nonlinear dynamic effects are a significant factor affecting the strength and durability of structures. Nonlinear elastic moduli of solids, are very sensitive to changes in the microstructure. Recording characteristics of nonlinear waves can be tracked very subtle changes in the internal structure of the material, which cannot be detected using traditional research methods. Analyzing of the resent research. 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 due to heterogeneity of the internal structure of the material has been studied less. Research objective. The aim of this work is devoted to finding the macroscopic wave equation describing the propagation of nonlinear elastic waves in fiber-reinforced composite materials in the case of non-ideal contact between the components. For this purpose– developed asymptotic method of averaging the highest order. Conclusions. In this paper a macroscopic wave equation describing the propagation of nonlinear strain waves in fiber composite in the case of non-ideal contact between the components was obtained. For this purpose, asymptotic method of higher order mode was developed. Antiplanar shear wave, propagating in a direction perpendicular to the axis of the fibers were observed. The effective elastic coefficients and the analysis of the numerical results obtained.