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Modal analysis of vocal folds models with descrete parameters
Lekeš, Filip ; Švancara, Pavel (referee) ; Hájek, Petr (advisor)
Bachelor’s thesis deals with modal analysis of computed models of human vocal folds. It’s about finite element and analytical model where values first eigenfrequencies come under male vocal folds. Research part applies to biomechanics of vocal the human voice, which is followed by an overview of computational models. Finite element model is completely created and solved by ANSYS Workbench commercial program, which uses the finite element method to simulate a problem. Solution of analytical model uses freely available Python programming language. Analysis of the results and comparison of approaches belong to main objectives of the presented work. The proposed analytical model can serve future students for detailed understanding of human vocal oscillations.
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Classical and fractional modelling of oscillatory motion
Hošek, Jaromír ; Tomášek, Petr (referee) ; Kisela, Tomáš (advisor)
In this thesis we deal with the issue of damped oscillations. Besides the classic description using member directly proportional to the first derivative position we focus on the model containing derivatives of non-integer order, so-called the fractional model of damped oscillations. The behavior of both models is studied through the test applications describing the movement of one, two, respectively three bodies connected by springs. The main tool for solving is the Laplace transform method. Besides the computational aspects we discuss some qualitative properties of solutions, especially dependence on order derivative in the fractional model and the behavior of the center of gravity system position.
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Experimentální určení tlumení nosníku
Fučík, Ondřej ; Hadraba, Petr (referee) ; Rubeš, Ondřej (advisor)
This bachelor thesis deals with structural damping of metallic materials. The first part is research of damping properties, ways how to discover damping properties and short description of how to simulate viscoelasticity of materials, using mathematical models. The second part is focused on an experiment with beams of different lengths and materials. Mathematical models making is also part of solution. The third, last part is focused on results processing. Using mathematical models, damping ratios of beams are determined.
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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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Experimentální určení tlumení nosníku
Fučík, Ondřej ; Hadraba, Petr (referee) ; Rubeš, Ondřej (advisor)
This bachelor thesis deals with structural damping of metallic materials. The first part is research of damping properties, ways how to discover damping properties and short description of how to simulate viscoelasticity of materials, using mathematical models. The second part is focused on an experiment with beams of different lengths and materials. Mathematical models making is also part of solution. The third, last part is focused on results processing. Using mathematical models, damping ratios of beams are determined.
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Speed of convergence of damped oscilations
Fara, Jakub ; Bárta, Tomáš (advisor) ; Pražák, Dalibor (referee)
We study solutions convergence of ordinary differential second order equation u′′(t)+ f(u′(t), t)u′(t) + |u|βu = 0, where β is a positive constant and f is a positive function. Physical meaning of this equation is one-dimensional damped oscilation with time va- riable environment resistance. We convert this studied function to the system of two equations of the first order. It enables us to proof the existence of some positively in- variant sets, hence we derive trajectory behaviour of solutions of this system. Thanks to that we will be able to do speed estimates of energy decrease for non-oscillation solution. Then in many cases we will be able to establish when the system solution for each time will oscillate or on the contrary when the oscillations will stop. 1
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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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Modal analysis of vocal folds models with descrete parameters
Lekeš, Filip ; Švancara, Pavel (referee) ; Hájek, Petr (advisor)
Bachelor’s thesis deals with modal analysis of computed models of human vocal folds. It’s about finite element and analytical model where values first eigenfrequencies come under male vocal folds. Research part applies to biomechanics of vocal the human voice, which is followed by an overview of computational models. Finite element model is completely created and solved by ANSYS Workbench commercial program, which uses the finite element method to simulate a problem. Solution of analytical model uses freely available Python programming language. Analysis of the results and comparison of approaches belong to main objectives of the presented work. The proposed analytical model can serve future students for detailed understanding of human vocal oscillations.
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|
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Classical and fractional modelling of oscillatory motion
Hošek, Jaromír ; Tomášek, Petr (referee) ; Kisela, Tomáš (advisor)
In this thesis we deal with the issue of damped oscillations. Besides the classic description using member directly proportional to the first derivative position we focus on the model containing derivatives of non-integer order, so-called the fractional model of damped oscillations. The behavior of both models is studied through the test applications describing the movement of one, two, respectively three bodies connected by springs. The main tool for solving is the Laplace transform method. Besides the computational aspects we discuss some qualitative properties of solutions, especially dependence on order derivative in the fractional model and the behavior of the center of gravity system position.
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