Problem of Vibration Damping in Mechanical Systems: System Analysis, Modeling, Control

System approaches are being developed in the problems of dynamics of transport and technological machines related to the provision of dynamic vibration damping modes and the identification of a number of specific effects characteristic of technical objects with working bodies representing solids. The methods of structural mathematical modeling are used, in which a mechanical oscillatory system, considered as a design scheme of a technical object, is compared with a structural scheme, equivalent in dynamic terms, of an automatic control system. It is shown that the modes of dynamic damping are realized through the fixation of fixed points called centers of rotation (or oscillations). A method is proposed for the analytical evaluation of the possibilities of forming dynamic states based on the use of generalized feedback transfer functions, coefficients of motion connectivity by coordinates, forms of dynamic interaction of system elements under the simultaneous action of two harmonic excitations. Within the framework of the interpretation under consideration, the key characteristic of a mechanical oscillatory system is the characteristic frequency equation and its transformations. The development of ideas about the form of dynamic interactions of elements of a mechanical oscillatory system is proposed. The concept of form generalizes ideas about the directions of change in time of the coordinate of a system element in relation to a change in an external force or kinematic excitation. The methodology for displaying a set of dynamic states and forms of dynamic interaction of elements of a mechanical oscillatory system based on oriented graphs is proposed.

1. Makhutov N. A. Safety and risks: system research and development, Novosibirsk, Nauka, 2017, 724 p. (in Russian).

2. De Silva C. W. Vibration. Fundamentals and Practice, Boca Raton, London, New York, Washington, D. C., CRC Press, 2000, 957 p.

3. Harris S. M., Cred C. E. Shock and Vibration Handbook, New York, McGraw — Hill Book Co, 2002, 1457 p.

4. Iwnicki S. Handbook of railway vehicle dynamics, CRC Press Taylor & Francis Group, 2006, 527 p.

5. Rocard Y. General Dynamics of Vibrations, Paris, Masson, 1949, 458 p.

6. Blekhman I. I. Theory of vibration processes and devices. Vibration mechanics and vibration technology, St. Petersburg, Publishing house "Ore and Metals", 2013, 640 p.(in Russian).

7. Panovko G. Ya. Dynamics of vibration technological processes, Moscow—Izhevsk, SIC "Regularic and chaotic dynamics", Institute of Computer Technologies, 2006, 176 p.(in Russian).

8. Galiev I. I., Nekhaev V. A., Nikolaev V. A. Methods and means of vibration protection of railway crews, Moscow, Publishing house of the Educational and Methodological Center for education on railway transport, 2010, 340 p. (in Russian).

9. Kolovsky M. Z. Automatic control of vibration protection systems, Moscow, Nauka, 1976, 320 p. (in Russian).

10. Korenev B. G., Reznikov L. M. Dynamic vibration dampers. Theory and technical applications, Moscow, Nauka, 1988, 304 p. (in Russian).

11. Karnovsky I. A., Lebed E. Theory of Vibration Protection, Springer International Publishing, Switzerland, 2016, 708 p.

12. Eliseev S. V., Lukyanov A. V., Reznik Yu. N., Khomenko A. P. Dynamics of mechanical systems with additional ties, Irkutsk, Irkutsk State University, 2006, 315 p.

13. Eliseev S. V., Reznik Yu. N., Khomenko A. P., Zasyadko A. A. Dynamic synthesis in generalized problems of vibration protection and vibration isolation of technical objects, Irkutsk, IGU, 2008, 523 p. (in Russian).

14. Eliseev S. V., Reznik Yu. N., Khomenko A. P. Mechatronic approaches in the dynamics of mechanical oscillatory systems, Novosibirsk, Nauka, 2011, 384 p. (in Russian).

15. Belokobylsky S. V., Eliseev S. V., Kashuba V. B. Applied problems of the structural theory of vibration protection systems, St. Petersburg, Polytechnic, 2013, 363 p.(in Russian).

16. Eliseev S. V., Artyunin A. I. Applied theory of oscillations in problems of dynamics of linear mechanical systems, Novosibirsk, Nauka, 2016, 459 p. (in Russian).

17. Eliseev S. V. Applied system analysis and structural mathematical modeling (dynamics of transport and technological machines: connectivity of movements, vibration interactions, lever connections), Irkutsk, IrGUPS, 2018, 692 p. (in Russian).

18. Eliseev S. V., Eliseev A. V. Theory of Oscillations. Structural Mathematical Modeling in Problems of Dynamics of Technical Objects. Series: Studies in Systems, Decision and Control, vol.252, Springer International Publishing, Cham, 2020, 521 p.

19. Eliseev A. V., Kuznetsov N. K., Moskovskikh A. O. Dynamics of machines. System representations, block diagrams and connections of elements, Moscow, Innovative Mechanical Engineering, 2019, 381 p. (in Russian).

20. Eliseev S. V., Eliseev A. V., Bolshakov R. S., Khomenko A. P. Methodology of system analysis in the tasks of evaluation, formation and management of the dynamic state of technological and transport machines, Novosibirsk, 2021, 679 p. (in Russian).

21. Lurie A. I. Operational calculus and application in technical applications, Moscow, Nauka, 1959, 368 p. (in Russian).