Application of Perturbation Theory of Non-Linear Systems to an Amplifier Circuit for EMI Analysis

Zupan, Dominik

doi:10.1109/emccompo.2019.8919872

Cited by 1 publication

(4 citation statements)

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“…The most effective methods of investigation of oscillating processes in nonlinear systems [14][15][16][17] with concentrated masses and distributed parameters are those based on introductory provisions of perturbation methods [18][19][20][21][22][23], combined with the principle of simultaneity of oscillations.…”

Section: Review Of Related Workmentioning

confidence: 99%

“…Below we consider only differential equations which describe the laws of change of amplitude and frequency of torsional oscillations of a flexible body, i.e., the system of differential equations (19). Its right-hand sides are 2 periodic…”

Section: Cos ( )mentioning

confidence: 99%

“…As follows from the first equation of the system (19), the amplitude of oscillations is proportional to the small parameter  . This means that during natural or forced oscillations, the amplitude changes by the value of the order  .…”

Section: Cos ( )mentioning

confidence: 99%

“…This means that during natural or forced oscillations, the amplitude changes by the value of the order  . This is the basis for using the averaging apparatus for differential equations (19) for the phases of natural oscillations and "reduced" pulse perturbation. Thus, in the non-resonant case, the main parameters of torsional oscillations of a nonlinear flexible body are described by the correlations…”

Section: Cos ( )mentioning

confidence: 99%

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Impulse Moments Influence on Single-Frequency Torsional Oscillations of Nonlinear Flexible Bodies

et al. 2022

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A method of analytical study of the influence of impulse moments on nonlinear torsional oscillations of a homogeneous constant cross-section of a body under classical boundary conditions of the first, second, and third types have been developed. When the flexible material properties meet the body close to the power law of flexibility, mathematical models of the process have been obtained. They are the boundary value problems for an equation of hyperbolic type with a small parameter at the discrete righthand side. The latter expresses the effect of pulse momentum on the oscillatory process. Under the effect of periodic pulse momentum on a flexible body, resonant and non-resonant processes are possible, and resonant processes occur when the amplitude of natural oscillations approaches a fixed value. The peculiarities of resonant oscillations are established. Relative torsional oscillations of a nonlinear flexible body that rotates around the axis with a constant portable angular velocity are considered, taking into account the periodic action of pulse momentum acting in a fixed cross-section. It is shown that: the amplitude of passing through the main resonance is more significant for larger values of the nonlinearity parameter; the case of the action of pulse momentum closer to the middle of the body. If the initial perturbation amplitude is less than the amplitude at which the resonance occurs in the presence of only internal forces of viscous friction, the external periodic impulse moments of resonance processes have occurred. The reliability of the calculation formulas is confirmed by the fact that in the extreme case known from the literature, resources are obtained related to the dynamics of the respective objects under the continuous action of autonomous perturbation.

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