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Title:Razvejitve pri Van der Pol-Duffingovem nihalu
Authors:Pušenjak, Rudi (Author)
Files:URL http://www.dlib.si/details/URN:NBN:SI:doc-AW9EZL0V
 
Language:Slovenian
Work type:Not categorized (r6)
Typology:1.01 - Original Scientific Article
Organization:FS - Faculty of Mechanical Engineering
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
Year of publishing:2003
Publisher:Association of Mechanical Engineers and Technicians of Slovenia et al.
Number of pages:str. 370-384
Numbering:Letn. 49, št. 7/8
UDC:531.391:534.1:519.61/.64:530.16
ISSN on article:0039-2480
COBISS_ID:8489750 New window
NUK URN:URN:SI:UM:DK:AZFXINGI
Views:587
Downloads:36
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Categories:Misc.
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Record is a part of a journal

Title:Strojniški vestnik
Shortened title:Stroj. vestn.
Publisher:Zveza strojnih inženirjev in tehnikov Slovenije [et al.]
ISSN:0039-2480
COBISS.SI-ID:762116 New window

Secondary language

Language:English
Title:Bifurcations of the Van der Pol-Duffing oscillator
Abstract:The incremental harmonic balance method has proved to be an efficient tool for computing periodic oscillations in the analysis of nonlinear dynamical systems. It was developed into a form that enables the computing of steady-state periodic response with a dependence on various variable parameters. When the bifurcation process follows a sequence of period doublings, than the periodic response is composed of subharmonic solution of higher orders. When no more subharmonic solutions exist in the process of periodic doublings, than the periodic response becomes chaotic. The changing of the amplitudes of the periodic oscillation in dependence of the variable system parameters and the possible transition into chaos is shown in bifurcation diagrams. A general procedure for the construction of a bifurcation diagram is the used in van der Pol-Duffing oscillator for various kinds of parameters. It is proved that the van der Pol-Duffing oscillator processes, various kind of bifurcations, which can be analyzed by using suitable strategies.
Keywords:dynamics of material systems, vibration of bodies, incremental harmonic balance method, nonlinear dynamic systems, periodical oscillations, bifurcation diagrams, mechanics


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