- Tytuł:
- The stability conditions of the cubic damping Van der Pol-Duffing oscillator using the HPM with the frequency-expansion technology
- Autorzy:
- El-Dib, Y. O.
- Powiązania:
- https://bibliotekanauki.pl/articles/122293.pdf
- Data publikacji:
- 2018
- Wydawca:
- Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
- Tematy:
-
homotopy perturbation method
nonlinear oscillators
cubic nonlinear damping van der Pol’s equation
nonlinear frequency analysis
stability analysis
metoda perturbacji homotopii
HPM
homotopijna metoda perturbacyjna
oscylator Van der Pol-Duffing
analiza stabilności
teoria perturbacji
oscylator nieliniowy
analiza częstotliwościowa - Opis:
- 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.
- Źródło:
-
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 31-44
2299-9965 - Pojawia się w:
- Journal of Applied Mathematics and Computational Mechanics
- Dostawca treści:
- Biblioteka Nauki
Artykuł