Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia:

L. I. Blekhman, Head of Laboratory, Candidate of Engineering Sciences, liblekhman@yandex.ru

Operating procedures in mineral mining and processing, in construction, in chemical and food industries, etc. are connected with haulage and conversion of a huge amount of granular and multicomponent materials. The singularity of vibration in these procedures consists in its ability to change, apparently, properties of granular materials and suspensions. For instance, a granular medium, subject to the intensity of vibrations, can behave as a solid, a viscous fluid or a gas. Vibration diminishes effective dry friction coefficients down to zero and induce additional, so-called vibrational forces which can be utilized beneficially. This article briefly reviews achievements of the Mekhanobr’s School in the sphere of theory of vibrations, engineering of new vibration machines and technologies, and R&D implementation at a full scale. The fundamental basis of the recent advances was laid in the previous decades owing to the development of the vibratory displacement theory, discovery of the phenomenon of self-synchronization of rotating bodies, as well as elaboration of vibration mechanics and vibration rheology approaches—new analytical methods to study influence of vibrations on nonlinear systems and media. The latest achievements are the generalization, improvement and implementation of these methods in solving variety of urgent applied problems. Engineering of new high-performance vibration machines for processing natural materials and waste (crushers, mills, sifts, etc.) is in progress. The current high-level R&D results are grounded on the work of many generations of Mekhanobr’s disciples.

1. Blekhman I. I., Dzhanelidze G. Yu. Vibrational displacement. Moscow : Nauka, 1964. 410 p.
2. Nagayev R. F. Periodic modes of vibrational displacement. Moscow : Nauka, 1978. 160 p.
3. Blekhman I. I. Synchronization of dynamic systems. Moscow : Nauka, 1971. 896 p.
4. Blekhman I. I. Synchronization in Science and Technology. New York : ASME Press, 1988. 255 p.
5. Nagaev R. F., Gezev V. V. Self-synchronization of inertia vibration exciters. Leningrad : Mashinostroenie, 1990. 178 p.
6. Nagaev R. F. Quasi-conservative synchronizing systems. Saint-Petersburg : Nauka, 1996. 251 p.
7. Blekhman I. I. Vibrational Mechanics. Moscow : Fizmatlit, 1994. 400 p.
8. Selected Topics in Vibrational Mechanics. Series A. Series on Stability, Vibration and Control of Systems. New Jersey : World Scientific, 2004. Vol. 11. 415 p.
9. Blekhman I. I. Theory of vibration processes and facilities : Vibration mechanics and vibration engineering. Saint-Petersburg, 2013. 639 p.
10. Blekhman I. I. Vibrational mechanics and vibrational rheology: theory and applications. Moscow : Fizmatlit, 2018. 751 p.
11. Nagaev R. F. Месhаniсаl Prосеsses with Rереаtеd Attenuated Impacts. Singapore : World Scientific Publishing Co. Pte. Ltd., 1999.
12. Vaisberg L. A. Design and calculation of vibrating screens. Moscow : Nedra, 1986. 144 p.
13. Vaisberg L. A., Zarogatskiy L. P., Turkin V. Ya. Vibratory crushers. Basics of calculation, design and technological application. Saint-Petersburg : Izdatelstvo VSEGEI, 2004. 306 p.
14. Ivanov N. A. Inertia cone crushers. Theory, engineering, design, operation. Saint-Petersburg, 2012. 128 p.
15. Anakhin V. A., Pliss D. A., Monakhov V. N. Vibration separators. Moscow : Nedra, 1991. 157 p.
16. Vaisberg L. A., Kartavy A. N., Korovnikov A. N. Screening surfaces of screens. Design, materials, application experience. Saint-Petersburg : Izdatelstvo VSEGEI, 2005. 252 p.
17. Arsentiev V. A., Vaisberg L. A., Zarogatsky L. P., Shuloyakov A. D. Production of cuboid crushed stone and Bbuilding sand using vibrating crushers. Saint-Petersburg : Izdatelstvo VSEGEI, 2004. 112 p.
18. Kartavy A. N. Vibration assemblies for mineral and waste material processing. Modeling and pieces of computation by energy- and resource-efficiency criteria : tutorial. Moscow : Izdatelstvo MGGU, 2013. 328 p.
19. Sorokin V. S. On the unlimited gain of a nonlinear parametric amplifier. Mechanics Research Communications. 2014. Vol. 62. pp. 111–116.
20. Kremer E. Sl ow motions in systems with fast modulated excitation. Journal of Sound and Vibration. 2016. Vol. 383. pp. 295–308.
21. Belyaev A. K ., Blekhman I. I., Polyanskiy V. A. Equation for the evolution of trapped hydrogen in an elastic rod subjected to high-frequency harmonic excitation. Acta Mechanica. 2016. Vol. 227, Iss. 5. pp. 1515–1518.

22. Lurie K. A. An Introduction to the Mathematical Theory of Dynamic Materials. Series: Advances in Mechanics and Mathematics. 2^nd ed. Cham : Springer, 2017. Vol. 15. 277 p.
23. Blekhman I. I. Frequency Synchronization and Its Possible Role in Microworld Phenomena. Automation and Remote Control. 2020. Vol. 81, No. 8. pp. 1405–1412.
24. Blekhman I. I., Semenov Yu. A., Yaroshevych M. P. On the Possibility of Designing Adaptive Vibration Machinery Using Self-synchronizing Exciters. Advanced Technologies in Robotics and Intelligent Systems : Proceedings of ITR 2019. Series: Mechanisms and Machine Science. Cham : Springer, 2020. Vol. 80. pp. 231–236.
25. Blekhman I. I., Vasilkov V. B., Semenov Yu. A. Vibrotransporting of Bodies on a Surface with Non-Translational Rotational Oscillations. Journal of Machinery Manufacture and Reliability. 2020. Vol. 49, No. 4. pp. 280–286.
26. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B. Energy Performance of Vibrational Transportation and Process Machines. Proceedings of the 14^th International Conference on Vibration Problems. Series: Lecture Notes in Mechanical Engineering. Singapore : Springer, 2021. pp. 29–46.
27. Kremer E. Vibrational Mechanics of Systems with Amplitude and Phase Modulation of Excitation. Nonlinear Dynamics of Structures, Systems and Devices : Proceedings of the First International Nonlinear Dynamics Conference. Cham : Springer, 2020. Vol. 1. pp. 35–41.
28. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B., Yakimova K. S. “Anomalous” Phenomena in Fluid under the Action of Vibration. Doklady Physics. 2008. Vol. 53, No. 10. pp. 520–524.
29. Blekhman I. I., Blekhman L. I., Sorokin V. S., Vasilkov V. B., Yakimova K. S. Surface and volumetric effects in a fluid subjected to high-frequency vibration. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2012. Vol. 226, Iss. 8. pp. 2028–2043.
30. Blekhman I. I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B., Yakimova K. S. Nonlinear Effects Observed in the Flow of a Fluid out of Vibrating Vessels. Doklady Physics. 2003. Vol. 48, No. 7. pp. 355–358.
31. Demidov I., Mikhailova N., Yasinskaya A., Samukov A. Development of the theory of vibratory injection of gas into liquid. Vibroengineering PROCEDIA. 2020. Vol. 32. pp. 216–222.
32. Blekhman I. I., Vaisberg L. A. Toward a theory of vibrational segregation. Obogashchenie Rud. 2014. No. 5. pp. 35–40.
33. Vaisberg L. А., Demidov I. V., Ivanov K. S. Mechanics of granular media under vibration action: the methods of description and mathematical modeling. Obogashchenie Rud. 2015. No. 4. pp. 21–31. DOI: 10.17580/or.2015.04.05
34. Blekhman I. I., Blekhman L. I., Vaisberg L. А., Vasilkov V. B., Yakimova K. S. On Vibrational Diffusion Segregation in Granular Media. Doklady Physics. 2016. Vol. 61, No. 1. pp. 8–10.