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Mathematical models of linear and nonlinear oscillators
Lovas, David ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor thesis deals with mathematical models of linear mechanical oscillators, which represent one of basic applications of ordinary differential equations. There are explained harmonic oscillators, damped oscillators and driven oscillators. The thesis discusses also superposition of oscillators and coupling of oscillators, including their synchronization.
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Mutual interaction of pressure pulsations and pulsations of undirect pipe
Hrazdíra, Zdeněk ; Pochylý, František (referee) ; Habán, Vladimír (advisor)
This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.
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TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Papáček, Štěpán ; Matonoha, Ctirad
Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
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Mathematical models of linear and nonlinear oscillators
Lovas, David ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor thesis deals with mathematical models of linear mechanical oscillators, which represent one of basic applications of ordinary differential equations. There are explained harmonic oscillators, damped oscillators and driven oscillators. The thesis discusses also superposition of oscillators and coupling of oscillators, including their synchronization.
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|
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Mutual interaction of pressure pulsations and pulsations of undirect pipe
Hrazdíra, Zdeněk ; Pochylý, František (referee) ; Habán, Vladimír (advisor)
This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.
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