Modeling of External Dynamics of Frictional Interaction Using the Elastic System Stability Theory

Musalimov, Victor; Nuzhdin, K.A.

doi:10.3103/s1068366619010136

Cited by 3 publications

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“…The results can be generalized to large number of layers with different properties and geometry. Such generalization will allow developing new mathematical models that are directly relevant to real technical products [11][12][13].…”

Section: Resultsmentioning

confidence: 99%

“…we find a solution in the area I for the second rod, considering that 1 motion from the area of rest in this case is separated by the front sought as in the from(3) by the characteristic method.Condition for keeping the quantity of movement on the front The scheme of finding a solution.If t then the motion quantity condition taking into account the solution in the area ( ) and(12) are valid in the area I so far as velocity of both rods align on the line:…”

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Mathematical Modeling of Impact of Possible Shock Dynamic Loads on the Modern Composite Materials

et al. 2019

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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.

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confidence: 99%

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confidence: 99%

Mathematical Modeling of Impact of Possible Shock Dynamic Loads on the Modern Composite Materials

et al. 2019

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“…The use of methods for solving the equations of mathematical physics in combination with precise formulations of problems in the mechanics of a deformable solid body allows creating new technological solutions for which modern viscoplastic and composite materials can be used. Such materials are necessary for the implementation of new design solutions, since they have low material consumption [6,7]. It is clear that modern structures created from modern viscoplastic and composite materials should work reliably in the elastic and viscoelastic regions under complex dynamic loads [8,9].…”

Section: Discussionmentioning

confidence: 99%

Mathematical Modeling of Vibration Dampers of Vibration-Insulated Structures

et al. 2021

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Vibration dampers are installed on the machine foundations in order to reduce the vibration level. Such technological solutions are most expedient in the case of a harmonic load with a low instability of the vibration frequency. Unfortunately, dampers do not provide such a large reduction in the dynamic effect on the base, as vibration isolation, but in some cases their efficiency turns out to be quite sufficient with a relatively simple implementation and low manufacturing cost. The use of dynamic vibration dampers gives a great effect when an increased vibration of foundations occurs during the operation of equipment in metallurgical production, for example, when processing materials by pressure, reconstructing enterprises and replacing heavy equipment. During the operation of heavy forging equipment and manipulators for various purposes, the foundations of these devices can be considered as a rigid body. The model soil on which this foundation is installed can be considered a homogeneous elastic isotropic half-space. When calculating with such mathematical models, one can use solutions of the corresponding dynamic contact problems. A comparative analysis of the effectiveness of damping foundation vibrations using different foundation models, including the model of an elastic, homogeneous half-space and a system of semi-infinite rods, the modulus of elasticity of which increases with depth according to the quadratic law, shows a fairly close agreement.

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Effective Directions of Development of the Method of Artificial Bases for Evaluating the Volumetric Wear Resistance of Materials

Efremov

2022

Mechanics and Control of Solids and Structures

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Modeling of External Dynamics of Frictional Interaction Using the Elastic System Stability Theory

Cited by 3 publications

References 1 publication

Mathematical Modeling of Impact of Possible Shock Dynamic Loads on the Modern Composite Materials

Mathematical Modeling of Impact of Possible Shock Dynamic Loads on the Modern Composite Materials

Mathematical Modeling of Vibration Dampers of Vibration-Insulated Structures

Effective Directions of Development of the Method of Artificial Bases for Evaluating the Volumetric Wear Resistance of Materials

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