|
|
Stability analysis of delay differential equations
Pustějovský, Michal ; Opluštil, Zdeněk (referee) ; Tomášek, Petr (advisor)
This thesis deals with asymptotic stability analysis of delayed differential equations. First we focus on introduction of this type of equations. Next we study stability of linear autonomous equations. Here we get some simple criteria of stability. The main part of the thesis is application of these criteria to a engineering problem - the model of turning tool regenerative effect. In mathematical sense, it is a initial value problem of linear delayed differential equation. Practical outcome of this thesis is a computer application written in Maple environment displaying stability region.
|
|
|
Description of Failure of the Multilayer Polymer Structure
Zouhar, Michal ; Klusák, Jan (referee) ; Kučera, Jaroslav (referee) ; Hutař, Pavel (advisor)
The aim of this thesis is to describe behavior of cracks in layered polymer materials. Quasi-brittle fracture (through the initiation and subsequent crack propagation mechanism) under low stresses is the most common mode of failure of polymer materials. In this case plastic deformations are localized in the vinicity of the crack tip and linear elastic fracture mechanics description of the crack behavior can be used. The knowledge of fracture parameters change during the crack propagation in multilayer body is a key point for establishing of the maximum load and consequently for the assessment of the residua lifetime. In contrast to homogeneous bodies the estimation of stress intensity factors for multilayer (composite) structure is numerically more elaborated and the fracture mechanics approach is complicated by the existence of interfaces between single layers, where material parameters are changed by a step. Special attention is paid to the configuration of a crack growing close to the material interface and along the interface. For the crack with tip on the material interface the effective values of stress intensity factor based on the crack stability criteria are estimated. It is shown that under special conditions (depending mainly on the elastic mismatch of materials) the existence of material interface has positive influence on the lifetime of the multilayered structure.
|
|
|
Description of Crack Propagation in the Fields of Strongly Non-Homogeneous and Residual Stresses
Štegnerová, Kateřina ; Materna, Aleš (referee) ; Malíková, Lucie (referee) ; Náhlík, Luboš (advisor)
This Ph.D. thesis was written under the supervision of Assoc. Prof. Luboš Náhlík, Ph.D. and Assoc. Prof. Pavel Hutař, Ph.D. Thesis is focused mainly on application of generalized linear elastic fracture mechanics, which allows description of crack behaviour propagating from general singular stress concentrators, such as material interfaces or sharp V-notches, and verification of validity of used fracture criteria. The obtained results were used in the next part of the thesis, which deals with the issue of crack propagating in ceramic composites, where the stress distribution field is strongly influenced by the existence of material interface and presence of residual stresses, that arise during manufacturing process of composite.
|
|
|
Linear system stability analysis
Jelen, Michal ; Jeřábek, Jan (referee) ; Koton, Jaroslav (advisor)
This bachelor’s thesis will be dealing with stability analysis of linear systems. In theoretical part will be mentioned stability and its conditions, stability criteria, their partition to groups and description of each criterion. In practical part will be chosen one stability criterion which will be working with afterwards. As examined circuit will be a filter with current conveyors as active elements which will be obtained a characteristic multinomial from. There will be working with transmittion functions of single and double pole model in examples. It will be created a computer programme which will enable an automatization of Routh’s stability criterion and plot graphical outputs in dependence on input parameters and their values.
|
|
|
Description of Crack Propagation in the Fields of Strongly Non-Homogeneous and Residual Stresses
Štegnerová, Kateřina ; Materna, Aleš (referee) ; Malíková, Lucie (referee) ; Náhlík, Luboš (advisor)
This Ph.D. thesis was written under the supervision of Assoc. Prof. Luboš Náhlík, Ph.D. and Assoc. Prof. Pavel Hutař, Ph.D. Thesis is focused mainly on application of generalized linear elastic fracture mechanics, which allows description of crack behaviour propagating from general singular stress concentrators, such as material interfaces or sharp V-notches, and verification of validity of used fracture criteria. The obtained results were used in the next part of the thesis, which deals with the issue of crack propagating in ceramic composites, where the stress distribution field is strongly influenced by the existence of material interface and presence of residual stresses, that arise during manufacturing process of composite.
|
|
|
Linear system stability analysis
Jelen, Michal ; Jeřábek, Jan (referee) ; Koton, Jaroslav (advisor)
This bachelor’s thesis will be dealing with stability analysis of linear systems. In theoretical part will be mentioned stability and its conditions, stability criteria, their partition to groups and description of each criterion. In practical part will be chosen one stability criterion which will be working with afterwards. As examined circuit will be a filter with current conveyors as active elements which will be obtained a characteristic multinomial from. There will be working with transmittion functions of single and double pole model in examples. It will be created a computer programme which will enable an automatization of Routh’s stability criterion and plot graphical outputs in dependence on input parameters and their values.
|
|
|
Description of Failure of the Multilayer Polymer Structure
Zouhar, Michal ; Klusák, Jan (referee) ; Kučera, Jaroslav (referee) ; Hutař, Pavel (advisor)
The aim of this thesis is to describe behavior of cracks in layered polymer materials. Quasi-brittle fracture (through the initiation and subsequent crack propagation mechanism) under low stresses is the most common mode of failure of polymer materials. In this case plastic deformations are localized in the vinicity of the crack tip and linear elastic fracture mechanics description of the crack behavior can be used. The knowledge of fracture parameters change during the crack propagation in multilayer body is a key point for establishing of the maximum load and consequently for the assessment of the residua lifetime. In contrast to homogeneous bodies the estimation of stress intensity factors for multilayer (composite) structure is numerically more elaborated and the fracture mechanics approach is complicated by the existence of interfaces between single layers, where material parameters are changed by a step. Special attention is paid to the configuration of a crack growing close to the material interface and along the interface. For the crack with tip on the material interface the effective values of stress intensity factor based on the crack stability criteria are estimated. It is shown that under special conditions (depending mainly on the elastic mismatch of materials) the existence of material interface has positive influence on the lifetime of the multilayered structure.
|
|
|
Stability analysis of delay differential equations
Pustějovský, Michal ; Opluštil, Zdeněk (referee) ; Tomášek, Petr (advisor)
This thesis deals with asymptotic stability analysis of delayed differential equations. First we focus on introduction of this type of equations. Next we study stability of linear autonomous equations. Here we get some simple criteria of stability. The main part of the thesis is application of these criteria to a engineering problem - the model of turning tool regenerative effect. In mathematical sense, it is a initial value problem of linear delayed differential equation. Practical outcome of this thesis is a computer application written in Maple environment displaying stability region.
|
guest ::
