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Title:Numerično modeliranje nelinearnega vsiljenega nihanja
Authors:ID Petek, Marko (Author)
ID Fajmut, Aleš (Mentor) More about this mentor... New window
ID Grešovnik, Igor (Comentor)
Files:.pdf UNI_Petek_Marko_2013.pdf (907,79 KB)
MD5: 16508190D7FA08EE59E32C2104F6CCFC
 
Language:Slovenian
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V diplomskem seminarju obravnavamo resonančno krivuljo magnetnega nihala, ki je primer nelinearnega oscilatorja. Najprej predstavimo analitično rešljiv primer linearnega oscilatorja in zatem numerično analiziramo oblike resonančnih krivulj magnetnega nihala. Ugotovimo, da se obnaša podobno, vendar ne enako, kot Duffingov oscilator s trdo vzmetjo. Resonančna krivulja se pri visokih amplitudah vsiljevanja nagne v desno in ima pri nekaterih vrednostih frekvence vsiljevanja dve možni amplitudi. Numerično izračunano resonančno krivuljo magnetnega nihala primerjamo z eksperimentalno izmerjeno krivuljo, a ujemanje ni zadovoljivo. Eksperimentalnemu obnašanju se približamo, če v matematičnem modelu Hookovo vzmet zamenjamo s trdo vzmetjo. Orodje za numerično analizo nihal je avtorsko delo, zato na koncu predstavimo tudi uporabljene algoritme in preverimo njihovo natančnost ter zanesljivost.
Keywords:nelinearni oscilator, nelinearna resonanca, Duffingov oscilator
Place of publishing:Maribor
Publisher:[M. Petek]
Year of publishing:2013
PID:20.500.12556/DKUM-42126 New window
UDC:53(043.2)
COBISS.SI-ID:20301576 New window
NUK URN:URN:SI:UM:DK:NW3BNLIW
Publication date in DKUM:30.01.2014
Views:3113
Downloads:221
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Numerical modelling of nonlinear driven oscillators
Abstract:The purpose of this BSc thesis is to study the resonance curve of a specific nonlinear oscillator (magnetic oscillator). First, the analytically solvable case of linear resonance is presented, then a numerical analysis of the resonance behaviour of the magnetic oscillator is peformed. We find out, that its behaviour is similar, but not equal, to the Duffing oscillator with a hardening spring. At higher driving amplitudes the resonance curve tilts to the right and becomes multivalued. The numerically calculated resonance curve is compared to the experimentally measured curve. The agreement is unsatisfactory. We are able to achieve better agreement with experimental results if we consider a hardening spring instead of the Hookean spring in the mathematical model. Finally, the algorithms used in numerical analysis are presented. The numerical oscillator analysis tool is author's own work, therefore its accuracy and reliability are tested.
Keywords:nonlinear oscillator, nonlinear resonance, Duffing oscillator


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