Nihanje zgradbe zaradi potresa : delo diplomskega seminarja

Travnik, Klara (author), Jaklič, Gašper (mentor)

V delu diplomskega seminarja problem nihanja zgradbe zaradi potresa modeliramo s sistemom diferencialnih enačb 2. reda. Spremenljivke sistema so masna in togostna matrika ter matrika dušenja. Potres opišemo s funkcijo. V sklopu reševanja modela vpeljemo posplošeni problem lastnih vrednosti (GEP) ter Cholesky QR algoritem kot način reševanja slednjega. Podrobneje si ogledamo tudi kvadratni problem lastnih vrednosti (QEP) in reševanje z linearizacijo. Predstavimo pojav resonance ter nihanje zgradbe pokažemo na primeru.

• Language: Slovenian
• Keywords: kvadratni problem lastnih vrednosti, nihanje, posplošeni problem lastnih vrednosti, potres, resonanca, sistem diferencialnih enačb
• Work type: Bachelor thesis/paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-149389
• UDC: 519.6
• COBISS.SI-ID: 163657731
• Publication date in RUL: 07.09.2023

Secondary language

• Language: English
• Title: Vibration of a building due to earthquake

Abstract

In this thesis we model the problem of vibration of a building due to earthquake with a system of second order differential equations. The variables of the system are a mass, stiffness and damping matrix. The earthquake is described with a function. Within solving the model, we introduce generalized eigenvalue problem (GEP) and Cholesky QR algorithm as a way to solve the latter. We also look into quadratic eigenvalue problem (QEP) and solving with linearization. We introduce the phenomenon of resonance and show an example of vibration of a building.

• Keywords: quadratic eigenvalue problem, vibration, generalized eigenvalue problem, earthquake, resonance, system of differential equations