https://sci.ldubgd.edu.ua/jspui/handle/123456789/12504 2026-04-04T12:54:46Z https://sci.ldubgd.edu.ua/jspui/handle/123456789/13685 Title: Побудова найкоротших кільцевих маршрутів у пакеті Maple Authors: Сало, Олена; Чмир, Оксана Юріївна 2023-01-01T00:00:00Z https://sci.ldubgd.edu.ua/jspui/handle/123456789/13684 Title: Список праць Authors: Чмир О.Ю. 2023-01-01T00:00:00Z https://sci.ldubgd.edu.ua/jspui/handle/123456789/12509 Title: Determination of frequency of transverse oscillations of an elasticly fixed disc of a circular saw Authors: Dziuba, Lidiia; Chmyr, Oksana; Menshykova, Оlha; Lishchynska, Khrystyna Abstract: The object of the study is a circular saw blade. An annular plate of constant thickness with a free outer contour and a fixed inner contour was taken as the calculation scheme of the saw blade. The real conditions for fixing the internal circuit correspond to the elastic fixing of the saw blade with clamping flanges on the shaft of the machine. For the accepted calculation scheme of the circular saw, the dynamic model was a fourth-order nonlinear differential equation of the transverse oscillations of the annular plate with the corresponding boundary conditions. The rotation of the circular saw was taken into account in the dynamic model due to the radial force in the middle surface of the ring plate. This force arises as a result of the action of centrifugal forces during the rotation of the saw blade. The solution to the fourth-order nonlinear differential equation was constructed using the Bubnov-Galyorkin numerical method. The boundary conditions for constructing the solution were as follows: the outer contour of the saw disk was considered free; the inner contour of the saw disk – elastically fixed with a certain stiffness coefficient. The solution was implemented in the Maple 15 mathematical environment in the form of a developed program. According to the obtained frequency equation, the values of cyclic and natural frequencies of transverse oscillations of circular saw disks of different thicknesses with the same radius of the inner contour and three values of the radii of the outer contour were determined: 150 mm, 200 m, and 250 mm. The effect of the rigidity of the internal contour fixing and the angular speed of rotation of the saw blade on the natural frequencies of transverse oscillations was studied. The study was performed for saw disks in the case of oscillations with one, two, and three nodal diameters. It was established that the rigidity of the internal contour of the saw blade has the greatest influence on the natural frequency of transverse oscillations with one nodal diameter Description: 1. The solution to the nonlinear differential equation of the transverse vibrations of the stretched disk of a circular saw was constructed using a numerical method under the following boundary conditions: the outer contour of the saw disk is free; the inner contour is elastically fixed. The frequency equation was obtained and the natural frequencies of transverse oscillations of circular saw blades of different thickness with the same radius of the inner contour and three values of the radii of the outer contour were determined. 2. The impact of the rigidity of the internal contour of the circular saw disk and the angular speed of its rotation on the change in the natural frequency of transverse oscillations was analyzed. It was established that with an increase in the rigidity of the internal contour fixation by 1000 N/m, the natural frequencies of oscillations of saw disks for one nodal diameter increase to 27.2 %. For transverse oscillations with two or three nodal diameters, changes in the natural frequencies of disk oscillations at the considered in the work stiffness values are insignificant (up to 1 % decrease in frequency). For oscillations with one nodal diameter, the angular speed of rotation of the saw blade increases its own frequency of transverse oscillations to 33.93 %. 2023-01-01T00:00:00Z https://sci.ldubgd.edu.ua/jspui/handle/123456789/12508 Title: До використання математичної статистики для прогнозування ризиків інформаційної безпеки Authors: Дзюба, Лідія Федорівна; Чмир, Оксана Юріївна 2023-01-01T00:00:00Z