Stochastic Mechanics (FSI-RSO)

Academic year 2018/2019
Supervisor: doc. Ing. Radek Vlach, Ph.D.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The aim of course is insight into stochastic mechanic meaning in engineering and integration to modeling of technical systems. It demand: make clear of knowledge of mathematical statistics and probabilistic theory, basic features of steady and unsteady phenomena, basic features of steady random processes algebra, basic features of modeling possibilities of operative and random processes, knowledge of basic method of dynamic systems responses solving.
Learning outcomes and competences:
Students can solve simple stochastic problems after the course. Students will have basic knowledge for following studies this field.
Prerequisites:
Basic terms of mathematical statistics and probabilistic, basic theory of mechanics, theory of dynamic systems and theory of technical systems.
Course contents:
Statistical techniques play indispensable roles in the fields of engineering disciplines, as well as in meteorology, biology and medicine. In this course we discuss the structure of probability space, characteristics of random data, probability function, correlation and spectral density functions, system identification and response, and basic engineering applications of correlation and spectral analysis.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Exam is written. Students get ahead topics. Oral exam will be in case irresolution.
Controlled participation in lessons:
Attendance at practical training is obligatory. Accreditation requirements are attendance on the practice and good results from all courses. Teacher defines concrete requirements in first practice.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Computer-assisted exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture Stochastic mechanics, their features in engineering and their aims
Basic terms of mathematical statistics and probabilistic
Analyse of process in the technical systems
Basic theory of dynamic systems
Steady and unsteady processes, deterministic chaos
Basic features of steady phenomena, algebra of steady processes
Models of unsteady processes and their phenomena
Correlation and spectral analysis and their features in engineering
Solving of simple stochastic problems in the time and spectral domain
Solving of simple stochastic problems in the time and spectral domain
    Computer-assisted exercise Basic problems of probabilistic theory
Basic problems of probabilistic theory
Computation of steady processes features
Computation of steady processes features
Computation of statistic characteristics of simple problems
Computation of statistic characteristics of simple problems
Computation of responses characteristics for dynamics problems – passage random signal with one degree of freedom
Computation of responses characteristics for dynamics problems – passage random signal with one degree of freedom
Responses of mechanical systems with more inputs and more outputs
Responses of mechanical systems with more inputs and more outputs
Literature - fundamental:
1. Kratochvíl, C. a kol.: Stochastická mechanika, I. Část, studijní podpory FSI, Ústav mechaniky, mechatroniky a biomechanika, 2004
2. Bolotin, V.V.: Použití metod teorie pravděpodobnosti a teorie spolehlivosti při navrhování konstrukcí. SNTL - nakladatelství technické literatury, Praha, 1978. (299 s)
3. Bendat, J., Piersol, A.: Engineering applications of correlation and spectral analysis, New York, Wiley-Interscience, 1980. 315 p
4. Kropáč, O.: Náhodné jevy v mechanických soustavách, SNTL Praha, 1987
5. Sun, J.: Stochastic Dynamics and Control, Elsevier, 2006
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
M2A-P full-time study M-MET Mechatronics -- Cr,Ex 5 Compulsory 2 2 W
M2A-P full-time study M-IMB Engineering Mechanics and Biomechanics -- Cr,Ex 5 Compulsory 2 2 W