We study the process of nonmonotonic loading of the deformable filler in a cylindrical shell with regard for the Coulomb friction. A numerical-analytic description of the loop of structural damping is obtained by using applied models.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 [6]. 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. A comprehensive survey of works devoted to the investigation of dynamic systems with various laws of friction can be found in [9]. 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. The general approaches to the formulation and solution of these problems developed for simplified one-dimensional models are described in [2]. The statements, methods, and solutions of some problems from this class and the results of experimental investigations can be found in [1,3,5,7,8]. Engineering methods for the numerical analysis of shell vibroinsulators were developed on the basis of the asymptotic analysis of the obtained solutions in [6].In the present work, we develop methods for the investigation of the stress-strain state, compliance, and damping ability of "cylindrical shell-deformable filler" systems used to model the main elastic element of vibration-protecting devices.Consider an elastic deformable cylinder (filler) of radius R and length 2a placed into a cylindrical shell with thickness h 0 (Fig. 1). The filler is compressed on the end faces by perfectly rigid pistons subjected to the action of an external load Q nonmonotonic as a function of time.

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Розроблено інженерну методику розрахунку напруженого стану та міцно-сти двошарових кераміко-алюмінійових покриттів, навантажених цуп-ким індентором. Досліджено вплив товщини оксидного шару на величину допустимого довільно орієнтованого навантаження. Розраховано оптима-льну товщину оксидного шару, яка забезпечує найбільший спротив пок-риття індентуванню.Ключові слова: плазмово-електролітичне оксидування, індентування, мі-цність, двошарове покриття, кераміка, алюміній.An engineering methodology for calculating both the stress state and the strength of the double-layer ceramic-aluminium coatings loaded with a hard indenter is developed. Influence of the oxide-layer thickness on the permissible arbitrarily oriented loading value is studied. An optimal thickness of the Corresponding author: Lyubomyr Yaroslavovych Ropyak

Розвинуто інженерну методику розрахунку утримувальної здатності твердих тіл з поверхневими тріщиноподібними дефектами, залікованими шляхом наплавлення неконтрастного шару. У аналітичній формі встановлено кількісні залежності ефективності наплавлення від товщини нанесеного шару, від глибини заповнення тріщини та від тріщинотривкості використовуваного матеріалу. Ключові слова: поверхнева тріщина, наплавлення, гранична рівновага. The engineering method of calculating the retention capacity of solids with superficial crack-like defects recovered by surfacing non-contrast layer is developed. In the analytical form, quantitative dependences of the surfacing efficiency on the thickness of the renovation layer, on the depth of feeling of the crack and on crack growth resistance of the using material are determined.

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A deformation model of underground pipeline under complicated geotechnical conditions of soil local fracture is proposed. The effect of displacement discontinuities and rotations of foundation blocks on the stressed state and limit equilibrium of pipe has been studied.Introduction. The service of underground pipelines in the areas of anomalous behavior of the foundation (waterlogged and marshy terrains, karst cavities or temporary workings, regions of freezing-thawing, soil settlement and slip, zones of tectonic faults, neotectonics or bench formation, earthquake and mudflow hazardous regions) involves nonstandard working conditions and requires an additional analysis together with engineering-geological monitoring and the use of rheological soil mechanics models. In spite of the diversity of these models [1][2][3][4], it is difficult to foresee the mechanical load on the pipeline in anomalous areas. To increase the safety of pipeline systems laid in mountaineous regions, it is necessary to develop engineering methods and models of the calculation of stress state and deformation of pipelines in the zones of local destruction of the bedrock foundation.Formulation of the Problem. The investigations were carried out in a geometrically and physically linear formulation. The pipeline was modeled by an infinite straight tubular rod (Fig. 1), which interacts with the bedrock through a backfill layer, which is described by the linearly elastic Winkler model. In more detailed consideration of strength issues, the pipe was taken as a membrane shell. Reciprocal displacements and rotations of bedrock blocks were described by discontinuous or piecewise differential functions. This approach allows one to determine pipeline stresses not from the distribution of earth load, which is usually difficult to estimate, but from the kinematic parameters of bedrock displacements.To quantitatively realize this concept, a boundary problem has been formulated: