Vibrations in engineering and technology

Kaletnіk Grigory Mikolayovich – academician of the NAAS of Ukraine, Doctor of Economics, Professor, Head of the Department of Administrative Management and Alternative Energy Sources of Vinnitsa National Agrarian University (Soniachna Str., 3, Vinnitsa, Ukraine, 21008).

Tsurkan Oleh Vasylovych – Candidate of Technical Sciences, Associate Professor, Director of Ladyzhyn College of Vinnytsia National Agrarian University (Petro Kravchik St., 5, Ladyzhyn, Vinnytsia Region, Ukraine, 24321, e-mail: tsurkan_ov76@ukr.net).

The method of formalizing a granular medium in the form of a continuous deformable medium provides that the granular medium is continuous. In this case, the methods of mechanics of continuous deformable media in Eulerian or Lagrangian coordinates are used. The method allows you to take into account the interaction between particles in the form of elastic, viscous or plastic components of internal resistance. With this formalization, the most widespread application of the Navier-Stokes equation. Unfortunately, the exact correct solution of such an equation in an analytical form does not exist.

It should be noted that the most common method is formalization in the form of a loose discrete medium. It can be used under conditions when the dimensions of the element, in which the changes in the kinematic and dynamic parameters are determined, exceed by at least an order of magnitude the maximum size of a fraction of a granular medium. With this formalization, you can use the methods of mechanics of granular discrete media.

When solving the problems of dynamics of motion of a loose discrete medium, it becomes necessary to compose the equations of its statics, which are necessary to solve the problems of dynamics. This is because the static equations allow one to supplement the boundary conditions and provide nonzero solutions for the problems of oscillations of a loose discrete medium, since during oscillations of such a medium zero values of quantities determined (density and velocity components of displacements) can occur at points where their functions intersect the zero line relative to which oscillating motion occurs.

The article describes the conditions of the static state of a granular medium in a working chamber, which are an addition to the boundary conditions when solving the problems of oscillations of a granular discrete medium, which is formalized as continuous with a significant manifestation of dry friction.

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