1. Razvejitve pri Van der Pol-Duffingovem nihaluRudi Pušenjak, 2003, original scientific article Abstract: Metoda končnega harmonskega ravnovesja se je izkazala za učinkovito orodje pri računanju periodičnih nihanj v analizi nelinearnih dinamičnih sistemov. Razvili smo jo v obliko, ki omogoča izračun ustaljenega periodičnega odziva v odvisnosti od različnih spremenljivih parametrov. Kadar razvejitveni postopek sledi zaporedju podvojitev period, je periodični odziv sestavljen iz subharmoničnih rešitev višjih stopenj. Ko v postopku podvojitev period ne obstajajo več nobene subharmonične rešitve, se periodični odziv spremeni v kaotičnega. Spreminjanje amplitud periodičnega nihanja v odvisnosti od spremenljivih parametrov sistema in s tem možen prehod v kaos prikazujemo v razvejitvenih diagramih. Splošni postopek konstrukcije razvejitvenega diagrama je uporabljen pri van der Pol-Duffingovem nihalu za različne vrste parametrov. Izkaže se, da se pri van der Pol-Duffingovem nihalu pojavi vrsta različnih razvejitev, ki jih je mogoče analizirati le z uporabo ustreznih strategij.
Keywords: dinamika materialnih sistemov, nihanje teles, metoda koračnega harmonskega ravnovesja, nelinearni dinamični sistemi, periodična nihanja, razvejitveni diagrami, mehanika
Published in DKUM: 10.07.2015; Views: 1335; Downloads: 69
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3. Extended Lindstedt-Poincare method for non-stationary resonances of dynamical systems with cubic nonlinearitRudi Pušenjak, 2008, original scientific article Abstract: This paper presents the extended Lindstedt-Poincare (EL-P) method, which applies multiple time variables to treat non-stationary oscillations arising in dynamical systems with cubic nonlinearities due to the slowly varied excitation parameters. The method is applied extensively in research of non-stationary vibrations of clamped-hinged beams. Recognizing the aperiodic nature of non-stationary oscillations, the new formulation is presented by adding an additional, slow time scale beside time scales of the nonlinear system, which generally correspond to the incommensurate nonlinear frequencies of the response. Using this concept, a generalized approach of the study to the passage through fundamental, superharmonic and subharmonic resonances is presented in the paper. Effects of slowly varying excitation frequency and slowly varying excitation amplitude on the non-stationary oscillations are studied with the computation of deviations from the stationary response. Although the method is formulated for N-dof dynamical systems having weak cubic nonlinearities, it is applied for non-stationary vibrations, where two-mode shape approximation of damped and undamped clamped-hinged beam, respectively, is used and the simultaneous appearance of internal resonance is taken into account. Stability analysis of stationary solutions is performed and comparisons of stationary resonance curves by results obtained with the incremental harmonic balance (IHB) method show good agreement. The passage through the fundamental resonance of damped and undamped clamped-hinged beam, respectively, is investigated in detail.
Keywords: dynamical systems with cubic nonlinearities, nonlinear oscillations, nonstationary nonlinear oscillations, time scales, excitation frequency, resonance, Lindstedt-Poincare method
Published in DKUM: 01.06.2012; Views: 2114; Downloads: 37
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5. Discussion on: "Analysis of control relevant coupled nonlinear oscillatory systems"Rudi Pušenjak, Maks Oblak, 2008, original scientific article Abstract: The paper by I. D. Landau et al. presents an analysis of two structures of coupled van der Pol oscillators done by using the Krylov-Bogoliubov (K-B) averaging method. They devise the K-B method to effectively compute self-excited and externally driven oscillations, respectively on systems presumably subjected to control, where amplitudes and phases are slowly varying functions of time. After they present feedback structures of single and coupled generalized van der Pol equations, respectively, they perform the K-B analysis of these equations, which results in explanation of various regimes of self-excited and externally driven oscillations including the analysis of the combustion instability model. Although the proposed K-B methodmay be considered as a step forward in modeling self-oscillating systems, this discussion wants to show, that problems solved by the K-B method can be treated also in an alternative way. Based on the paper [1], it is obvious that coupled van der Pol oscillators, driven by an external excitation with slowly varying frequency or amplitude, can be analyzed by using Extended Lindstedt- Poincare (EL-P) method with multiple time scales.
Keywords: van der Pol oscillators, external excitation, multiple time scales
Published in DKUM: 31.05.2012; Views: 1623; Downloads: 71
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6. Upravljanje procesa izgorevanja v Rijkejevi ceviRudi Pušenjak, Maks Oblak, 2008, published scientific conference contribution Abstract: Članek obravnava upravljanje neustaljenih nihanj avtonomnega nihala z eno prostostno stopnjo, kakršna se pojavljajo v procesu izgorevanja v Rijkejevi cevi. Upravljanje procesa izgorevanja v Rijkejevi cevi modeliramo z van der Polovim nihalom. Za obravnavo neustaljenih nihanj je v članku uporabljena razširjena Lindstedt-Poincarejeva (EL-P) metoda z več časovnimi skalami. S pomočjo te metode ugotovimo, da so neustaljena nihanja skoraj periodična, amplituda in faza nihanj pa funkciji počasne časovne skale. Brez upravljanja dotoka goriva je proces izgorevanja nestabilen in samovzbujena nihanja težijo k limitnemu ciklu. Z upravljanjem dotoka goriva zadušimo samovzbujena nihanja, s čemer dosežemo asimptotično stabilno stanje.
Keywords: avtonomno nihalo, neustaljeno nihanje, zgorevanje, Rijkejeva cev, numerični rezultati
Published in DKUM: 31.05.2012; Views: 2224; Downloads: 43
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