- Zelenskaya, Т.S. and Siasiev, А.V., The dynamic problem of the longitudinal wave propagation in the steel ropes for elastic medium with variable borders. Вісник Дніпропетровського університету. – 2014. – Т. 22, вип. 18(1). – С. 58-62.
Considered initial-boundary value problem of mathematical physics that describes the longitudinal fluctuations of the rope variable length with a weight at the lower end. Provides a comparison of solutions using a modified method of continuation and numerical integration.
- Makarenkov, E.A. and Siasiev, А.V., Temperature field of cylinder with heat-insulated butt ends during heat exchange convection on the generatrix. Вісник Дніпропетровського університету. – 2015. – Т. 23, вип. 19(1). – С. 58-62.
To consider different elements of constructions, which are used in mechanical engineering, the attention can be paid to the fact that components, in the form of a thick-walled hollow cylinder, which cross-section is a doubly connected area, are used in these elements. The high-temperature speed gas or liquid flow, passing through the inner cavity, creates uneven heating, defined both by conditions of the flow and feature of design. The research arising through this complex thermostressed state is important in the design of mechanical engineering things. Taking into account the fact that we often have to deal with short-term impact of high temperatures, it is important to study unsteady temperature fields to determine their greatest unevenness. The latter thing can give rise to the thermostressed state, leading to disturbance of the operating mode. The proposed paper deals with the task of spreading the heat in the circular cylinder with defined radius and height with the specified starting temperature. The bases of the cylinder are heat-insulated, and along the generatrix is forced heat exchange with the environment. A mathematical statement of the internal problem that satisfies the heterogeneous equation of thermal conduction and homogeneous mixed condition on the generatrix of the cylinder is given. The solution of the problem is carried out by factorization using finite integral transforms of the mixed problem of mathematical physics to the cylinder.
- Zelenskaya, Т.S. and Siasiev, А.V., Investigation of the accuracy of the approximate solution of the mixed problem for hyperbolic equations on metabolic processes in vertical vessels. Машинобудування: Збірник наукових праць. 2015. № 15. С. 71-75.
The aim of this work is to compare the dynamic performance of wave processes in longitudinal movement of the rope through the production and numerical calculations, and obtain the equation of state of the rope on the pulley winding and outside of the pulley. The problem of elastic displacements in vertical vessels, was reduced to a boundary value problem with variable structure for hyperbolic equations, and the boundary between the different structures is movable. Analytical solution and its numerical realization is obtained in quadratures in the form of longitudinal waves propagating in the rope. Analysis of the solution of the problem shows that the distribution of the contact stresses on the surface of the rope (at a constant distance from the region of localization of the external load) practically does not depend on the distribution of the normal load in the area of localization only if its width is less than the thickness of the rope wound on the pulley. A significant influence on the dynamic tension in the vertical ropes have longitudinal movement, reflected from the moving region.
- Zelenskaya, Т.S. and Siasiev, А.V., DYNAMICS OF ELASTIC DYSPLACEMENTS OF LONGITUDINAL OSCILLATIONS IN ROPES AND CORES WITH MOBILE BORDERS. Машинобудування: Збірник наукових праць. 2012. № 10. С. 74-84.
Initial boundary value problems are considered for ropes and cores that change length throughout some interval of operation of the mechanism. Character of reflections of longitudinal waves from the mobile end are investigated.
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