Model of self-oscillations without harmonicas of the base frequency
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 53-59
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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.
Keywords:
self-oscillatory system, harmonious linearization, discrete time, difference equations, harmonious approximation of speed, spectrum of self-oscillations.
@article{VSGU_2018_24_3_a6,
author = {V. V. Zaytcev and E. Yu. Fedyunin},
title = {Model of self-oscillations without harmonicas of the base frequency},
journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
pages = {53--59},
publisher = {mathdoc},
volume = {24},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a6/}
}
TY - JOUR AU - V. V. Zaytcev AU - E. Yu. Fedyunin TI - Model of self-oscillations without harmonicas of the base frequency JO - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ PY - 2018 SP - 53 EP - 59 VL - 24 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a6/ LA - ru ID - VSGU_2018_24_3_a6 ER -
%0 Journal Article %A V. V. Zaytcev %A E. Yu. Fedyunin %T Model of self-oscillations without harmonicas of the base frequency %J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ %D 2018 %P 53-59 %V 24 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a6/ %G ru %F VSGU_2018_24_3_a6
V. V. Zaytcev; E. Yu. Fedyunin. Model of self-oscillations without harmonicas of the base frequency. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 53-59. http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a6/