Vibrations in engineering and technology

Dubchak Viktor– Ph.D., Associate Professor of the Department of Mathematics, Physics and Computer Technologies of Vinnitsa National Agrarian University (Pirogov St., 111/21, Vinnitsa, Ukraine, 21037, e-mail: viktor_dubchak@rambler.ru).\

The study of this work is a continuation of some previous results. The issue of filling certain external geometric objects or structures with a homogeneous set of other objects, in particular, a rounded shape, is an urgent task for solving a number of problematic issues in the field of agro-industrial production, storage and transportation of products of the appropriate geometric shape. The problem of effective maximum filling of containers of various geometries when storing products, bunker storages is always an urgent task not only in agricultural production, but also in the field of mechanical engineering, pharmaceuticals, furniture industry, military logistics, etc.

As a result of research conducted on the modeling of technological processes of filling high-tech working bodies with geometric structures in the form of loose materials of spherical shape, in the research data, unlike the previous results, the emphasis is placed on the use of mathematical models of external three-dimensional geometric structures. For these structures, the introduction of similar to the flat case of fillings, the utility coefficient of such a maximum filling, was proposed and tested. In the case of three-dimensional geometric objects, this indicator is set as the ratio of the maximum possible useful volume to the entire volume of the external geometric structure that is to be filled (in percent). The value of this coefficient for standard three-dimensional geometric bodies or structures is calculated and the corresponding results are given. In this work, as supporting material, relevant drawings, tabular values as an illustration of individual formula results, and brief conclusions of the conducted research are given.

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