Course detail

Stochastic Mechanics

FSI-RSOAcad. year: 2013/2014

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.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Radek Vlach, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Learning outcomes of the course unit

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.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

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.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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.

Specification of controlled education, way of implementation and compensation for absences

Accreditation requirements are attendance on the practice and good results from all courses. Teacher defines concrete requirements in first practice.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Bendat, J., Piersol, A.: Engineering applications of correlation and spectral analysis, New York, Wiley-Interscience, 1980. 315 p
Bolotin, V.V.: Použití metod teorie pravděpodobnosti a teorie spolehlivosti při navrhování konstrukcí. SNTL - nakladatelství technické literatury, Praha, 1978. (299 s)
Kratochvíl, C. a kol.: Stochastická mechanika, I. Část, studijní podpory FSI, Ústav mechaniky, mechatroniky a biomechanika, 2004
Kropáč, O.: Náhodné jevy v mechanických soustavách, SNTL Praha, 1987
Sun, J.: Stochastic Dynamics and Control, Elsevier, 2006

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme N3901-2 Master's

    branch M-IMB , 2 year of study, winter semester, compulsory
    branch M-MET , 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.
prof. Ing. Přemysl Janíček, DrSc.
doc. Ing. Miloš Vlk, CSc.

Syllabus

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

13 hod., compulsory

Teacher / Lecturer

doc. Ing. Tomáš Návrat, Ph.D.
prof. Ing. Přemysl Janíček, DrSc.
doc. Ing. Miloš Vlk, CSc.

Syllabus

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