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ArticleName Patterns in averaging of nonlinear dependencies on oscillating parameters: applications to ore processing problems
DOI 10.17580/or.2023.05.07
ArticleAuthor Blekhman L. I.

Institute for Problems in Mechanical Engineering of RAS (Saint Petersburg, Russia)

Blekhman L. I., Leading Researcher, Candidate of Engineering Sciences,


Oscillations of parameters in mathematical formulas may change the average values of the functions for these parameters quite significantly. As the simplest example, harmonic oscillations of the radius of a spherical body (bubble), when compressed, increase its average volume and surface area, while the average radius remains unchanged. Despite their trivial nature, such considerations are often ignored, which may lead to inaccuracies and errors. Such effects are typical for any non-linear mathematical relations and are therefore essential for all areas of engineering. The objective of the work is to evaluate the significance of such effects when solving a specific technical problem and to identify their potential applications in ore processing and other technologies. It establishes the general patterns of such effects and provides examples for certain formulas of elementary mathematics and mathematical analysis. Applications to ore processing problems are also considered. In particular, the impact of changes in the initial parameters on the process efficiency and the impact of oscillations in the ore grade on the performance of the processing plant are assessed. The results of the study may be of interest for the theory of vibrational processes and devices, the theory of accuracy, as well as for the theory of control and optimal processes. The paper discusses the relation between the issues considered and problems of oscillatory effects on dynamic systems and the analogy with the mechanics of systems with hidden parameters.
This work was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (subject No. 121112500313-6).

keywords Oscillations of parameters, averaging, nonlinear relationships, mineral processing, ore blending, recovery, efficiency

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