Wyniki wyszukiwania - BazTech

1

The stability conditions of the cubic damping Van der Pol-Duffing oscillator using the HPM with the frequency-expansion technology

El-Dib Y. O.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

31--44

EN

In this paper, we perform the frequency-expansion formula for the nonlinear cubic damping van der Pol’s equation, and the nonlinear frequency is derived. Stability conditions are performed, for the first time ever, by the nonlinear frequency technology and for the nonlinear oscillator. In terms of the van der Pol’s coefficients the stability conditions have been performed. Further, the stability conditions are performed in the case of the complex damping coefficients. Moreover, the study has been extended to include the influence of a forcing van der Pol’ oscillator. Stability conditions have been derived at each resonance case. Redoing the perturbation theory for the van der Pol oscillator illustrates more of a resonance formulation such as sub-harmonic resonance and super-harmonic resonance. More approximate nonlinear dispersion relations of quartic and quintic forms in the squaring of the extended frequency are derived, respectively.

2

Impact and chaotic phenomena in nonlinear nonsmooth electrical dynamical systems

Trzaska Z.

Przegląd Elektrotechniczny

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2015

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R. 91, nr 4

77--85

EN

The article presents results of the analysis of nonlinear oscillators with nonsmooth elements and nonlinear systems with nonsmooth excitations. Main attention has been focused on highlighting specific properties of nonsmooth systems compared to their smooth counterparts. Nonsmooth transformation of the time variable and the replacement of initial issues by boundary problems have been taken as the base for the analytical method. Results of numerical simulations and computing in the form of graphs of voltage and current waveforms and attractors are presented.

PL

W artykule przedstawiono wyniki analizy nieliniowych oscylatorów z niegładkimi elementami oraz układów nieliniowych z niegładkimi wymuszeniami. Zasadnicza uwaga została skupiona na uwypukleniu specyficznych właściwości układów niegładkich w porównaniu do ich odpowiedników gładkich. Niegładką transformację zmiennej czasowej i zastąpienie zagadnień początkowych zagadnieniami brzegowymi przyjęto jako podstawę metody analitycznej. Przedstawiono wyniki symulacji numerycznych i obliczeń komputerowych w postaci wykresów przebiegów napięć i prądów oraz atraktorów.

3

On Noise Analysis of Oscillators Based on Statistical Mechanics

Thiessen T., Mathis W.

International Journal of Electronics and Telecommunications

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2010

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Vol. 56, No. 4

357-366

EN

In this paper a new approach of thermal noise analysis of electronic oscillators is presented. Although nonlinear electronic oscillators are one of the most essential subcircuits in electronic systems typical design concepts for these oscillators are based on ideas of linear circuits. Because the functionality of oscillators depends on nonlinearities, advanced design methods are developed where nonlinearities are an integral part. Since low voltage oscillator concepts have to be developed in modern IC technologies there is a need to include at least thermal noise aspects into the design flow. For this reason we developed new physical descriptions of thermal noise in electronic oscillators where we use ideas from nonequilibrium statistical mechanics as well as the Langevin approach. We illustrate our concepts by some examples.