Czech

5

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Absolvent bude mít znalosti v oblasti modelování nelineárních technických systémů a bude znát odezvy a projevy nelineárních dynamických systémů. Bude schopen linearizovat dynamický systém v okolí pracovního bodu. Bude schopen řešit úlohy technické praxe, které mohou být modelovány tímto způsobem. Absolvent bude seznámen s problematikou chaotického chování a stochastické mechaniky. Bude schopen analyzovat odezvy soustavy zatížené seismickou událostí a při zatížení náhodným buzením.

Linear algebra, differential equations, strength of materials, kinematics and dynamics of particles and bodies, solution of N degrees of freedom system oscillation, numerical methods of linear algebra and ODE solutions, MATLAB or Python programming.

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The course is taught through lectures explaining the basic principles and theory of the discipline. Seminars are focused on practical topics.

The course-unit credit is granted under the condition of active participation in seminars and gain at least 20 points of 40. The points can be obtained by elaboration of partial tasks and presentations. The gained points from the exercise is part of the final classification of the subject.
Final examination: The exam is divided into two parts. The evaluation of the exam is based on the classifications of each part. If one of the parts is graded F, the final grade of the exam is F. The content of the first part is a test, of which a maximum of 30 points can be obtained. The content of the second part is a solution of typical problems. It is possible to gain up to 30 points from this part. The form of the exam, types, number of examples or questions and details of the evaluation will be given by the lecturer during the semester. The final evaluation is given by the sum of the points gained from the exercises and exam. To successfully complete the course, it is necessary to obtain at least 50 points, where the maximum of 100 ECTS points can be reached.

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The aim of the course is to acquaint students with the specifics of behavior of nonlinear dynamic models in both frequency and time domain. Students will learn basic methods of solution by linearization of nonlinear models and numerical solutions. Students will also gain an overview of chaotic behavior, attractors, bifurcation and fractals. The aim of the second part of the course is to acquaint students with the basics of stochastic mechanics and to solve dynamic problems of random excitation and seismic events.

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. One absence can be compensated for by elaboration of substitute tasks

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Steven H. Strogatz: Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) 1st Edition, CRC Press, 2000. (EN)
Jinqiao Duan: An Introduction to Stochastic Dynamics (Cambridge Texts in Applied Mathematics) 1st Edition, 2015. (EN)

Not applicable.

eLearning: currently opened course

26 hours, compulsory

- Linear vs. nonlinear models
- Stability of dynamic systems
- Linearizing at an operating point
- Numeric solution of nonlinear system response
- Phase diagrams and attractors
- Self excited oscillations
- Bifurcation and chaos
- Typical tasks of stochastic mechanics
- Random vibrations in time domain
- Random vibrations in frequency domain
- Response of structure with seismic event excitation
- Response of model with random vibrations excitation
- Fatigue limit state at random vibrations

eLearning: currently opened course