Course objectives:
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To make sense of analytical and numerical modelling of discrete and continuous systems and its behaviour simulation, eigenfrequency and mode shape computation.
To acquaint with the use of numerical methods especially finite element method in dynamics and its application to beam, rotor, thin-walled and pipeline systems.
To acquaint with the direct numerical methods for integration of equations of motion in the time domain.
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Requirements on student
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Credit requirements: participation in laboratory practices
Examination requirements:
Active knowledge of lecturing problems and ready for use methods of computational mechanics
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Content
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1. Fundamental concepts from functional analysis and linear algebra
2. Methods of continuum discretization. Static and eigenvalue problems
3. Solution of the operator equations by means of modal method
Ordinary differential equations with constant coefficient matrices
Equations described by self-adjoint differential operators
4. Equations described by general differential operators
5. Eigenvalue problem solution
6. Methods of the direct numerical integration
7. FEM in the continuum dynamics
Longitudinal vibrations of bar
Torsional vibration of the bars having circular and annular cross section
8. Spatial vibration and stability of rotors
9. Rigid body-beam and piping system modelling
Straight beam and pipe finite elements
Beam and pipe arch-shaped finite elements
Rigid bodies, massless springs and dampers
10. Slender thin-walled finite elements
11. Thin walled plates and shells
12. Vibration and stability of the time periodic dynamical systems
13. Crack affect to the rotor behaviour and stability
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Activities
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Fields of study
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https://www.kme.zcu.cz/pro-studenty/modernizace-vyuky-ve-vybranych-predmetech-garantovanych-na-katedre-mechaniky-fav-zcu-v-plzni/modernizace-vyuky-predmetu-vypoctove-metody-mechaniky-kme-vmm
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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65
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Preparation for an examination (30-60)
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85
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Total
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150
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
orientovat se na úrovni základů diferenciálního a integrálního počtu |
orientovat se na úrovni základů teorie kmitání lineárních diskrétních systémů |
orientovat se v oboru mechaniky tuhých těles na úrovni základního kursu mechaniky vysokých škol technického směru |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
řešit odezvu dynamických lineárních systémů s jedním stupněm volnosti na libovolný typ buzení |
sestavit pohybové rovnice lineárních a nelineárních mechanických soustav s jedním a více stupni volnosti |
vypočítat vlastní čísla a vlastní pravostranné a levostranné vektory matic |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
orientovat se v metodách integrace pohybové rovnice pomocí modální metody |
orientovat se v metodách přímé numerické integrace pohybové rovnice |
orientovat se v metodách výpočtu vlastních čísel a vlastních frekvencí kmitavých soustav |
popsat tvorbu matematických modelů diskrétních a diskretizovaných kmitavých systémů ve tvaru soustavy obyčejných diferenciálních rovnic |
popsat tvorbu matematických modelů spojitých kmitavých systémů ve tvaru soustavy parciálních diferenciálních rovnic |
Skills - skills resulting from the course: |
analyticky řešit dynamickou odezvu lineárních kontinuí na libovolný typ buzení |
analyticky řešit odezvu lineárních kmitavých systémů s více stupni volnosti na libovolný typ buzení |
použít vybranou metodu přímé numerické integrace a vytvořit příslušné programové vybavení |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Skills - skills achieved by taking this course are verified by the following means: |
Oral exam |
Competences - competence achieved by taking this course are verified by the following means: |
Oral exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture with visual aids |
Skills - the following training methods are used to achieve the required skills: |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
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