Numerično modeliranje nelinearnega vsiljenega nihanja

diplomski seminar na bolonjskem študijskem programu 1. stopnje Fizika

Marko Petek (Author), Aleš Fajmut (Mentor), Igor Grešovnik (Co-mentor)

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

fizika;nelinearni oscilatorji;nelinearna resonanca;Duffingov oscilator;diplomski seminarji;

Data

Language:	Slovenian
Year of publishing:	2013
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Petek]
UDC:	53(043.2)
COBISS:	20301576
Views:	2315
Downloads:	163
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Numerical modelling of nonlinear driven oscillators
Secondary 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.
Secondary keywords:	nonlinear oscillator;nonlinear resonance;Duffing oscillator;
URN:	URN:SI:UM:
Type (COBISS):	Final seminar paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za fiziko
Pages:	22 str.
ID:	8727085