MODEL OF SELF-OSCILLATIONS WITHOUT HARMONICAS OF THE BASE FREQUENCY
- Authors: Zaitsev V.V.1, Fedyunin E.Y.2
-
Affiliations:
- Samara National Research University
- Joint-Stock Company Progress Rocket Space Centre
- Issue: Vol 24, No 3 (2018)
- Pages: 53-59
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/6453
- DOI: https://doi.org/10.18287/2541-7525-2018-24-3-53-59
- ID: 6453
Cite item
Full Text
Abstract
The nonlinearity of self-oscillatory system limiting amplitude of the generated signal is a source of the higher harmonicas of the base frequency. Harmonicas distort a form of self-oscillations and lower stability of their frequency. In the work the mathematical model of generation of self-oscillations, free from the highest harmonicas — strictly monochromatic self-oscillations is offered. The model is based on a method of equivalent (harmonious) linearization, popular in the applied theory of nonlinear oscillations. Numerical realization of the model in discrete time has allowed to formulate two algorithms of generation of monochromatic self-oscillations. One of them includes the procedure of numerical integration of a Cauchy problem for the system of ordinary differential equations. Another — reproduces processes in the discrete dynamic system designed on analog model-prototype. The monochromaticity of discrete self-oscillations is confirmed within the numerical experiment.
About the authors
V. V. Zaitsev
Samara National Research University
Author for correspondence.
Email: morenov@ssau.ru
E. Yu. Fedyunin
Joint-Stock Company Progress Rocket Space Centre
Email: morenov@ssau.ru
References
- Andronov A.A., Vitt A.A., Hajkin S.E. Teoriia kolebanii . M.: Nauka, 1981, 568 p. .
- Teodorchik K.F. Avtokolebatel’nye sistemy . M.: Gostekhizdat, 1952, 272 p. .
- Bogolyubov N.N., Mitropolsky Yu.A. Asimptoticheskie metody v teorii nelineinykh kolebanii. Izd. 4-e, ispr. i dop. . M.: Nauka, 1974, 504 p.
- .
- Kapranov M.V., Kuleshov V.N., Utkin G.M. Teoriia kolebanii v radiotekhnike . M.: Nauka, 1984, 320 p. .
- Zaitsev V.V., Stulov I.V. O vliianii podmenennykh garmonik na dinamiku avtokolebanii v diskretnom vremeni . Izvestiia vuzov. Prikladnaia nelineinaia dinamika , 2015, Vol. 23, no 6, pp. 40–46. DOI: http://doi.org/10.18500/0869-6632-2015-23-6-40-46 .