Course objectives:
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Student will be introduced with:
- methods of creation of condensed mathematical models of vibrating systems
- spectral tuning and sensitivity analysis
- definition of optimization tasks in dynamics of machines
- mathematical condition of optimality
- numerical methods of unconditioned and conditioned optimization
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Requirements on student
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Course recognition requirements: Working up course project. Exam evaluation: 100 per cent oral exam
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Content
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1.Repeting conditions of unconditional mathematical optimization.
2.Conditional optimization. Kuhn Tucker conditions. Lagrange multipliers.
3.Numerical methods for one-dimensional minimization.
4.Numerical methods for multidimensional zero order minimization.
5.Numerical methods for multidimensional first-order minimization. Newton's method.
6.Restrictive condition respecting. Penalty method. Gradient projection method.
7.Tuning parameters of mechanical systems. Linear approximation method.
8.Solving linear algebraic equations. Pseudoinverse matrix.
9.Objective functions and constraints in the optimization of vibrating mechanical systems.
10.Response spectrum and its calculation. Suppression of transient response.
11.One-dimensional continuum optimization in terms of weight.
12.Mathematical and physical condensation. Modal reduction. Guyan's reduction.
13.Reduction of systems consisting of subsystems. Use of secondary shapes.
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Activities
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Fields of study
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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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Preparation for an examination (30-60)
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50
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Contact hours
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65
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Graduate study programme term essay (40-50)
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40
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Total
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155
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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 v modelování kmitavých mechanických soustav |
definovat základní pojmy lineární algebry a maticového počtu |
vysvětlit pravidla hledání extrémů funkcí |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
řešit soustavy lineárních algebraických rovnic užitím maticového počtu |
analyzovat průběh funkce |
vytvořit matematický model konkrétní kmitavé mechanické soustavy |
orientovat se v numerických metodách a software pro řešení lineárních algebraických i diferenciálních rovnic |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
popsat pojmy a tvrzení podmíněné optimalizace funkcí |
vyjmenovat numerické metody optimalizace a popsat možnosti jejich použití |
popsat metody dynamické syntézy mechanických soustav a jejich frekvenčního přeladění |
orientovat se v metodách redukce počtu stupňů volnosti soustav |
Skills - skills resulting from the course: |
řešit úlohu podmíněné optimalizace zadané funkce analytickými metodami |
pro konkrétní úlohu snížení dynamického zatížení soustavy sestavit cílovou funkci, omezující podmínky a navrhnout metodu řešení optimalizační úlohy |
provést modální analýzu a analýzu citlivosti konkrétní kmitavé soustavy |
provést redukci počtu stupňů volnosti konkrétní kmitavé soustavy |
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 |
Individual presentation at a seminar |
Skills - skills achieved by taking this course are verified by the following means: |
Oral exam |
Individual presentation at a seminar |
Competences - competence achieved by taking this course are verified by the following means: |
Individual presentation at a seminar |
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 supplemented with a discussion |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture supplemented with a discussion |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture supplemented with a discussion |
Practicum |
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