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Main menu for Browse IS/STAG
Course info
KME / SM
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Course description
Department/Unit / Abbreviation
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KME
/
SM
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Statistical Mechanics
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech, English
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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2 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter + Summer
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Semester taught
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Winter + Summer
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Minimum (B + C) students
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10
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech, English
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
Yes
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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KME/MECH2 or KME/TM or KME/TMT
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Courses depending on this Course
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KME/AME, KME/DME, KME/SZAME, KME/SZDKM
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The student will be introduced with
- introduction to the response solution of the mechanical systems in frequency domain
- problem solution to behaviour of mechanical systems whose inputs or inner parameters have random character
- introduction to parameter identification of the vibrating systems based on measured input and output quantities
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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. Introduction to statistical mechanics. Dirac impulse, Fourier analysis
2. Bases of probability theory, random variable and its functions
3. Random processes, statistics of the 1-st and 2-nd order. Stationarity, ergodicity. moment generating function, correlation function, spectral density
4. Random processes generating using computer, generator of pseudo random processes, generating of pseudo random numbers with prescribed probability density and prescribed spectral density
5. Linear spatially discrete systems. Vibration of the linear discrete mechanical systems forced by random excitation. The use of modal method
6. Vibration of the linear discrete mechanical systems containing structural parameter imperfections excited by deterministic excitation
7. Random vibration of linear continuum
8. Regression, identification and tuning. Methods of spectral tuning and parameter identification
9. Random signal processing. Extreme analysis, structural failure. Structural durability estimation
10. Crossing level problems. Durability estimation of the structure loaded by narrow band excitation
11. Statical non-linear systems. Methods of statistical linearization.
12. Dynamic non-linear systems. Fokker-Planck equation assemblage. Probability density estimation of the response.
13. Numerical methods for solution to linear and non-linear discrete mathematical models
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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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80
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Contact hours
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52
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Total
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132
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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 základech diferenciálního a integrálního počtu z oblasti matematické analýzy |
orientovat se ve znalostech z oboru mechaniky tuhých těles na úrovni základního kursu mechaniky vysokých škol technického směru |
orientovat se základech maticového počtu a teorie pravděpodobnosti |
popsat základy teorie kmitání lineárních systémů |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
numericky integrovat diferenciální rovnice a soustavy rovnic popisující chování mechanických systémů s jedním a více stupni volnosti |
řešit elementární příklady z počtu pravděpodobnosti |
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: |
popsat postup, jak identifikovat parametry kmitavých systémů na základě experimentálně zjištěných vstupních a výstupních veličin |
popsat postup, jak určit spektrální reprezentaci vstupních budicích procesů, zejména spektrální hustotu a Fourierův obraz |
popsat postup, jak určit vybranou spektrální reprezentaci výstupních veličin, zejména spektrální hustotu a Fourierův obraz |
popsat postup sestavení pohybové rovnice diskrétních i spojitých mechanických systémů obsahujících náhodné parametry a popsat postup, jak tyto rovnice řešit zejména ve frekvenční oblasti |
Skills - skills resulting from the course: |
určit horní a spodní odhad výstupních veličin statických a dynamických systémů v pravděpodobnostním smyslu slova |
určit spektrální hustoty, matice kovariančních funkcí a vektor středních hodnot dynamických systémů se stacionárním ergodickým vstupem |
určit střední hodnoty a kovarianční matice statických systémů s jedním a více stupni volnosti |
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 |
Practicum |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
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