20.500.12556/RUL-155406 Analiza virov neharmoničnosti pri nihanju realne strune Analysis of sources of inharmonicity in the vibration of a real string V magistrskem delu smo raziskovali različne vplive, ki pri godalnih inštrumentih privedejo do odstopanja lastnih frekvenc strune od dobro znanih vrednosti, ki držijo za idealno struno. Ugotovili smo, da je vzrokov za pojav teh odstopanj (neharmoničnosti) kar precej, dosti modelov je že razvitih, večina predstavljenih modelov pa temelji na opustitvi neke predpostavke (poenostavitve), ki jo upošteva idealni model strune. Dodali smo še nov model, ki upošteva vpliv zunanje sile loka na lastne frekvence strune. Iz teorije lahko ugotovimo, da model skupne neharmoničnosti prav gotovo ni preprost, saj je ta odvisen od mnogo posameznih virov neharmoničnosti in posledično dokaj velikega števila spremenljivk. Eksperimenti za validacijo takšnega modela bi torej bili zelo obsežni, zato smo ga v tem delu predstavili le kvalitativno. Meritve dejanskih vrednosti lastnih frekvenc strune smo izvedli na kontrabasu, kjer smo za transformacijo zajetega zvočnega signala iz časovnega v frekvenčni prostor uporabili algoritem hitre Fourierove transformacije. Pri tem pa smo se osredotočili na A-struno, ki smo jo vzbujali z lokom in brenkanjem. Ugotovili smo, da je neharmoničnost izmerljiva in v slišnem področju ter da ima nova struna nižjo neharmoničnost kot stara struna. In our master's thesis, we explored various factors that lead to a deviation of the natural frequencies of the string in string instruments from the well-known values that are derived for an ideal string. We concluded that there are quite a few reasons for these deviations (inharmonicity) and that many models have already been developed. Most of those models challenge one of the assumptions that hold for an ideal string model. We also added a new model that takes into account the effect of the bow force on the natural frequencies of a string. From the theoretical part, we can conclude that a model for the total inharmonicity is by no means a simple one. The main reason for this is that it depends on many different sources of inharmonicity and many different variables. The number of experiments required to validate such a model would therefore be very extensive. For that reason, we concluded to only make a qualitative representation of the model. The actual frequencies of a real string were measured on a double bass. The sound signals we recorded were converted from the time to the frequency domain by means of a Fast Fourier Transform algorithm. When conducting the experiments, we focused on the A-string, which we excited by bowing and with pizzicato. We concluded that the level of inharmonicity is measurable and that it can also be heard. According to our experiments, the inharmonicity of a new string is lower than the inharmonicity of an old string. strune prizvoki robni pogoji neharmoničnost nelinearno vzbujanje velike amplitude Helmholtzovo gibanje strings overtones boundary conditions inharmonicity nonlinear excitation large amplitudes Helmholtz motion true false false [M. Zupet] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-03-30 07:30:14 2024-03-30 07:30:20 2024-04-08 10:31:40 0000-00-00 00:00:00 2024 0 Ljubljana 0 XXII, 55 str. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 534.141:534.63:780.614.31(043.2) 260046 191687683 32992.pdf 32992.pdf 1 ADEC46957B376769C408310A30BF561A 99493f8de61f98ff2f004c70ada43dc7e07b86c142f3ca3b3924fe368021f6a6 fb85570a-ee5e-11ee-8505-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=182274 Fakulteta za strojništvo 0 0 0