Mechanics
Проведено математическое описание модели зарождения трещины в полосе переменной толщины. Определение неизвестных параметров, характеризующих зародышевую трещину, сводится к решению системы сингулярных интегральных уравнений. Получено условие, определяющее критическое значение внешней нагрузки, при которой происходит трещинообразование.
Numerical and analytical aspects of generating
This paper describes a new variant of the averaging of the Navier–Stokes equations for axisymmetric flow of a viscous incompressible fluid with a minimum number of simplifying hypotheses. The complete system is spatially one-dimensional differential equations describing the dynamics of blood flow in the large arteries.
The motion of solid body with a small displacement mass center from the axis of dynamic symmetry has been studied. Analytical conditions for the existence of a hyperbolic singular point in the phase portrait of the system and the analytical solution for the separatrices have been obtained. Body makes a chaotic motion near separatrices under the influence of small perturbations caused by the asymmetry of the body.
Method of feedback parameters selection for gas jet stabilization systems with elastic roads, based on minimizing the mean square deviation of the real frequency response of the designed system with respect to the real desired frequency response, was implemented. The results of analysis of transient errors stabilization functions, taking into account the effect of time delay in gas jet executive stabilization systems are given.
Asymptotic integration of elasticity theory 3D equations is fulfilled for the case of multilayered arbitrary-shaped thin-walled shells. The tangential and the transverse long-wave low-frequency approximations are constructed. The governing 2D equations are derived.
The model of the continuum percolation of hard spheres with permeable shells, which describes phase transition sol-gel, has been investigate.
Small forced vibrations of growing cylindrical shell fixed on circular boundaries is studied in the framework of Kirchhoff–Love shell theory. The process of the accretion are characterized by the continuous adherence of material particles to its facial surface. Since the shell bends during the accretion, its stressed-strained state depends not only on loading, but also on the history of the process of accretion, i.e. the schedule of accretion.
