Control of Linear Inhomogeneous Systems by the Methods of Singular Integral Equations

Abstract

Mathematical models of linear inhomogeneous systems based on singular integral equations depending on the location of inhomogeneities are considered. The stress-strain state of a crack-like or rigid inclusion defect is estimated using the general application of the basic principles of the plane problem of the theory of elasticity, as well as the theory of functions of a complex variable or the method of singular integral equations. On the basis of singular integral equations with non-klemmanian displacement, the recommended dynamic models of physical phenomena that are formed in inhomogeneous media. The possibilities of improving the reliability and durability of the cylindrical group of technological methods, including the use of coatings from wear-resistant materials on the working surfaces of cylinders are considered. Finishing products with wear-resistant coatings lead to the formation of defects on the treated surfaces, reduce the performance characteristics of these products. Analysis of the causes of the formation of chips and cracks on the surfaces of these products to be processed showed that the appearance of these defects is associated with the thermal processes that accompany the mechanical treatment. An analytical model was developed to determine the thermomechanical state of the working surface of a cylinder with a wear-resistant coating. A tribocorrosion study of composite materials based on Ni/Ni-TiO₂ , obtained by the method of electrochemical deposition, was carried out. The simulation results using singular integral equations open up the possibility of an effective assessment of the effect of extraneous fillers on the loss of functional properties of inhomogeneous systems. In turn, a precise definition of the order and character of the singularity at the vertices of acute imperfections in a heterogeneous medium, pre-relations in an analytical form, is necessary to formulate and write the corresponding criterion relations for determining the functional properties of heterogeneous systems.