Abstract
In this paper, we study the dynamic processes in materials reinforced with fibers, that can be represented as composite rods. There has been developed a mathematical model of wave propagation under the impact of a shock pulse in semi-infinite composite rods. It is believed that the considered composite rod consists of two layers formed by simpler rods of different isotropic materials with different mechanical properties. The cross sections of such rods are considered to be constant and identical. When such composite materials are impacted by dynamic loads, a significant part of the energy is dissipated due to the presence of friction forces between the contact surfaces of the rods. In this regard, we study the propagation of waves in an elastic fiber-rod, the layers of which interact according to Coulomb law of dry friction. The case of instantaneous excitation of rods by step pulses is investigated. The blow is applied to a rod made of a harder material. In the absence of slippage, the friction force gets a value not exceeding the absolute value of the limit. In the absence of slippage, the friction force takes a value not exceeding the absolute value of the limit. Let us consider the value of the friction force constant. Normal stresses and velocities satisfy the equations of motion and Hooke’s law. The problem statement results in the solution of inhomogeneous wave equations by the method of characteristics in different domains, which are the lines of discontinuities of the solution. Solutions are found in all constructed domains. On the basis of the analysis of the obtained solution, qualitative conclusions are made and curves are constructed according to the obtained ratios. From the found analytical solution of the problem it is possible to obtain ratios for stresses and strain rates in composite rods and composite materials.
Highlights
Composites [1] in which the components are typically arranged at a certain frequency are of interest because of their ability to attenuate shock pulses [2]
The extreme complexity of the interaction of waves in the propagation of the shock pulse in the real composite material leads to the fact that modern theoretical methods of investigation of this problem are limited to strongly idealized models [3]
The new mathematical models must take into account wide variety of materials used and complicated interactions between layers that form a composite material
Summary
Composites [1] in which the components are typically arranged at a certain frequency are of interest because of their ability to attenuate shock pulses [2]. Pipelines may be located not just underground, where they may be subject to seismic shocks, and in more aggressive and corrosive environments, for example, sea water This necessitates the development of new materials and their mathematical models. The developers must consider the effects of friction conditions between layers, sliding of layers with respect to each other at macro-, micro, and nano-levels, and other intricate layer interaction effects while projecting and synthesizing new composite materials Modeling of such materials allows reaching the increased dependability and service life of new technological systems, including pipeline transport systems. In this work , a mathematical model of dynamic processes in materials reinforced with fibers, which are e represented by composite rods, has been developed When such materials are subject to dynamic loads, a significant portion of energy is dissipated due to friction forces between the contact surfaces of the rods. Force assumes a certain value not exceeding the absolute limit [10]
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