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Merjenje elastičnega modula visečega obroča
Pirnar, Kaja (Author), Brojan, Miha (Mentor) More about this mentor... This link opens in a new window

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Abstract
V zaključni nalogi se ukvarjamo z določitvijo elastičnega modula elastičnega obroča, ki se obešen na klin deformira zaradi lastne teže. V nalogi najprej izpeljemo glavno diferencialno enačbo problema, ki jo za zmerno velike pomike najprej rešimo s preturbacijsko metodo in za velike pomike - z metodo Runge Kutta 4. reda in strelsko metodo. Eksperimentalno pridobljene točke upogibnice obroča primerjamo z numerično izračunanimi, tako da spreminjamo vhodni podatek (modul elastičnosti) in spremljamo kdaj se obe krivulji najbolj ujemata. S takšnim postopkom določimo modul elastičnosti obroča. Izračunamo relativne napake med točkami krivulje, pridobljenimi eksperimentalno in numerično in opazimo dobro ujemanje. Na koncu primerjamo rezultate aproksimativnega in numeričnega izračuna krivulje obroča.

Language:Slovenian
Keywords:elastični moduli, obroči, lastna teža, upogibna togost, perturbacijska metoda, Runge Kutta 4. reda
Work type:Final paper (mb12)
Tipology:2.11 - Undergraduate Thesis
Organization:FS - Faculty of Mechanical Engineering
Year:2020
Publisher:[K. Pirnar]
Number of pages:XIII, 26 f.
UDC:539.32:621.887:519.6(043.2)
COBISS.SI-ID:31559683 Link is opened in a new window
Views:67
Downloads:21
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Secondary language

Language:English
Title:Measurement of elastic modulus of a hanging ring
Abstract:
In the final thesis we deal with determination of elastic modulus of a hanging elastic ring, which, deforms under self-weight. We first derive the main differential equation,which is solved by perturbation method for moderately large displacements and by 4th order Runge Kutta and shooting method for large displacements. We compare experimentally obtained points of the curve of a hanging ring to numerically calculated ones, and change the elastic modulus (unknown parameter) in the process to obtain the best match between the two methods. We calcutated the relative errors between the points of experimental and numerical curves and observe a relatively good match. We also compare the results of the approximative and numerical calculations.

Keywords:elastic moduli, elastic rings, self-weight, flexural rigidity, perturbation method, 4th order Runge Kutta

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