Vibrations in engineering and technology

Solona Olena – Candidate of Technical Sciences, Associate Professor of the Department of General Technical Disciplines and Labor Protection, Vinnytsia National Agrarian University (3, Solnyschaya St., Vinnytsia, Ukraine, 21008, e-mail: solona_o_v@ukr.net).
Kovbasa Vladimir Petrovich – Doctor of technical sciences, Professor of the Department of General Technical Disciplines and Labor Protection, Vinnytsia National Agrarian University (3, Solnyschaya St., Vinnytsia, Ukraine, 21008, e-mail: kovbasav@ukr.net).

This part of the article is a continuation of the first part of the article of the same name. The equations of boundary conditions, which are the displacements applied to the walls of the container are derived in this part. A system of hyperbolic equations with variable coefficients is obtained. It allows, together with the static equations given in Part 1, to obtain the values of the velocity components of the displacements of granular media in the container, as well as changes in its density, depending on the medium mechanical properties and the kinematic regimes of the applied displacements.
The numerical solution of this system of equations allows one to solve successively the equations on the determination of stress components both in the wall layers and in the absence of the action of the walls of the container.
The equations are given that allow us to determine the possible linear and angular displacements of concretions in the wall layers during the contact interaction of the concretion with the wall, and also in the absence of contact interactions taking into account the dynamic effect of the granular medium, that is moving. These functions are obtained for the most general cases, which include the granular medium's mechanical properties, the geometric dimensions, shapes and mechanical properties of the concretions and walls of the container, and the kinematic regimes of the impacts applied to the walls of the container.
The equations obtained are the initial ones for the numerical solution of the problems of displacements, changes in the density of the granular medium, and the possible linear and angular displacements of concretions that are in the medium.
Using finite elements method (FEM) or finite volumes method (DEM) it is possible to obtain final solutions of the equations. These equations make it possible to determine the kinematic regimes of the applied kinematic effects in order to obtain the necessary density changes and possible displacements of granular media, as well as the necessary displacements and velocities of these displacements concretions, which are in a moving granular medium.

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