MIXED PROBLEM OF FRICTIONAL INTERACTION OF A COAXIAL CYLINDRICAL SHELLS WITH AN ELASTIC FILLER - Popadyuk, I. Y. (Computer Science and Applied Mathematics, 2017)
In the contemporary industry, a significant role is played by vibrational processes. The operation of all machines and mechanisms without exception is directly connected with the appearance of vibrations. In most cases, vibrations decrease the strength, reliability, and durability of industrial machines, mechanisms, and structures and exert harmful influence on the health of the personnel. Thus, the problem of vibroinsulation proves to be quite urgent both from the viewpoint of engineering and for the labor protection. One of the ways used for the solution of the formulated problem is connected with the application of vibroprotecting devices, such as shock absorbers, dampers, dynamic vibration absorbers, etc. This is why the research and design works and theoretical investigations in the field of development of new means of vibroprotection and methods for their numerical analyses are of crucial importance. Note that new promising vibroinsulators were designed at the Pidstryhach Institute for Applied Problems in Mechanics and Mathematics on the basis of a new type of vibration-protecting devices based on the so-called shell elastic elements. As the main distinctive feature of structures of this type, we can mention the application of thin-wall elements (shells, plates, and bars) as the principal bearing and actuating elements. From the viewpoint of design, these are deformable shell systems with dry friction. In the mechano-mathematical modeling of the behavior of elastic elements under (generally speaking, nonmonotonic) loading, we get a class of nonlinear nonconservative mixed contact problems of the frictional interaction of thin shells with deformable fillers. Many boring devices of vibration insulation which are used for drilling of oil and gas wells are included an internal shell assigned for various technological requirements. That is why, the necessity of mechanical and mathematical modelling of system of a coaxial cylindrical shells divided by the elastic filler is existed. The mixed problem of frictional interaction in this system has been investigated in presented work with allowance for the Coulomb friction. The analytical description of the stress-strain state has been obtained by using the applied models. The obtained results make it possible to extend the range of applicability of the methods used for the numerical analyses of shell vibroinsulators and perform a more accurate analysis of the influence of the elastic characteristics of the materials of the shells and the filler on durability of the analyzed system.