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Matematična izpeljava in programska implementacija metode pLSCF za identifikacijo modalnih parametrov
ID Potočar, Primož (Author), ID Peperko, Aljoša (Mentor) More about this mentor... This link opens in a new window, ID Čepon, Gregor (Comentor)

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Abstract
Natančna identifikacija modalnih parametrov predstavlja ključen korak pri analizi dinamskega obnašanja mehanskih struktur. V ta namen so bile razvite številne eksperimentalne in numerične metode, katerih cilj je oceniti modalne parametre iz izmerjenih frekvenčnih odzivov sistema. V zadnjih desetletjih so pomemben razvoj doživele metode, ki temeljijo na kompleksni matrični polinomski aproksimaciji eksperimentalnih frekvenčnih prenosnih funkcij. V magistrskem delu se osredotočamo na eno izmed najrobustnejših tehnik tovrstne identifikacije, imenovano poli-referenčna metoda najmanjših kvadratov v kompleksni frekvenčni domeni. Po pregledu teoretičnega ozadja je podana lastna matematična izpeljava s podrobnim opisom posameznih korakov postopka. V nadaljevanju je predstavljena implementacija metode v programski kodi ter preverjanje njene pravilnosti na analitičnem dinamskem modelu. Dobljeni rezultati so primerljivi z referenčnimi vrednostmi, s čimer je verificirana implementirana koda.

Language:Slovenian
Keywords:LSCF, pLSCF, matrična aproksimacija, aproksimacija frekvenčne prenosne funkcije, metoda najmanjših kvadratov, identifikacija modalnih parametrov, faktorji modalnih prisotnosti, spremljevalna matrika, normirani polinomi
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FS - Faculty of Mechanical Engineering
Year:2025
Number of pages:XXII, 54 str.
PID:20.500.12556/RUL-175476 This link opens in a new window
UDC:512.643.12:512.622(043.2)
COBISS.SI-ID:256208899 This link opens in a new window
Publication date in RUL:29.10.2025
Views:106
Downloads:34
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Secondary language

Language:English
Title:Mathematical derivation and program implementation of the pLSCF method for modal parameter identification
Abstract:
Precise identification of modal parameters represents a key step in the dynamic analysis of mechanical structures. For this purpose, numerous experimental and numerical methods have been developed to estimate modal parameters from measured frequency response data. In recent decades, methods based on complex matrix polynomial approximation of experimental frequency transfer functions have undergone significant development. In this thesis, we focus on one of the most robust identification techniques, known as the Poly-reference Least Squares Complex Frequency method (pLSCF). After presenting the theoretical background, a detailed mathematical derivation of the method is provided. Furthermore, the implementation of the method in program code is presented and verified using a analytical dynamic model. The obtained results show good agreement with the reference values, confirming the accuracy of the implemented code.

Keywords:LSCF, pLSCF, matrix approximation, frequency transfer function approximation, least squares method, modal parameter identification, modal participation factors, companion matrix, monic polynomials

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