Random Oscillations of Nonlinear Dynamical Systems

AN Savoskin*
Russian University of Transport (MIIT), Moscow, Russia
*Corresponding Author: AN Savoskin, Russian University of Transport (MIIT), Moscow, Russia.

Published: March 29, 2023

DOI: 10.55162/MCET.04.126

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Abstract  

Real dynamical systems tend to contain individual elements with nonlinear characteristics. Such characteristics correspond to a number of elements:

• limiters, as well as devices with saturation of magnetic characteristics in electronic and electromagnetic systems;
• Rubber parts, vibration dampers, as well as leaf springs in mechanical systems , etc.

Therefore, when studying oscillations in such systems, it is necessary to take into account the nonlinearity and characteristics of individual elements and the features of oscillations inherent in nonlinear systems with such characteristics [13, 30]. The most significant features of nonlinear oscillatory systems are as follows:

• They do not apply the principle of superposition;
• Several equilibrium positions may exist in them;
• Their free oscillations are notizochronous, that is, the frequency of free oscillations depends on the initial conditions;
• They are ambiguous, that is, the results of the solution depend not only on the frequency, but also on the amplitude of the perturbations; it is possible to appear oscillations with frequencies of 2, 3, etc. times lower frequencies of the main oscillations - subharmonic oscillations, as well as with frequencies of 2, 3, etc. times higher frequencies of the main oscillations - superharmonic (ultraharmonic) oscillations.
• The possibility of the appearance of self-oscillatory modes, i.e. non-extinguishing oscillations even in the absence of an active perturbation, despite the presence of dissipative forces.