Display on the Phase Plane of the Slow Processes in Conservative Chains with One Degree of Freedom at Nonlinear Resonance
Authors: Sudakov V.F. | Published: 14.04.2015 |
Published in issue: #2(101)/2015 | |
DOI: 10.18698/0236-3933-2015-2-40-57 | |
Category: Radio Engineering and Communication | |
Keywords: nonlinear resonance, bistability, phase plane, phase portrait, special point on the phase plane |
The weakly nonlinear electric chains without resistors with a single source of harmonic excitation are discussed. Differential equations of the chains are identical to the typical nonlinear equation of second order. The amplitude of the excitation and its frequency detuning are small. The equations for the amplitude and phase of resonant oscillation are obtained by the method of averaging. A simple and effective method (applicable only in the case of conservative chains) is proposed for the analysis of amplitude-phase plane. Using it amplitude-frequency characteristic is presented and modes of one- and bistability are selected. The phase portrait corresponds to each mode: in the mode of one-stability it has one particular point, in the mode of bistability-three points. The coordinates of special points, the nature of their stability and phase trajectory in their surroundings are determined. In the mode of bistability the full phase portrait is built qualitatively and it enables to present transient processes at various initial conditions.
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