20.500.12556/DKUM-42126 Numerično modeliranje nelinearnega vsiljenega nihanja Numerical modelling of nonlinear driven oscillators 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. 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. nelinearni oscilator nelinearna resonanca Duffingov oscilator nonlinear oscillator nonlinear resonance Duffing oscillator true true false [M. Petek] Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2013-09-12 08:56:13 2014-01-30 12:37:05 2022-05-06 03:07:40 2021-04-25 03:17:41 2013 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 53(043.2) 20301576 URN:SI:UM:DK:NW3BNLIW UNI_Petek_Marko_2013.pdf UNI_Petek_Marko_2013.pdf 1 16508190D7FA08EE59E32C2104F6CCFC a1dc4c6785d622356845d603e4e45ea7c29c15c74a64e90b0367dcb078e0cc4c 51038a60-7c0a-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=58662 Fakulteta za naravoslovje in matematiko 0 0 0