Dynamics (FSI-5DT-A)

Academic year 2023/2024
Supervisor: doc. Ing. Stanislav Věchet, Ph.D.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
The objective of the course Dynamics is to familiarize students with basic principles of mechanics as well as methods applied for dynamic solving of mechanical systems. The emphasis is on understanding the physical principles governing motion of rigid bodies and applying them to solve simple technical problems in practice.
Learning outcomes and competences:
Dynamics deals with the relationship between motions and forces. Students will be able to analyze motion equations of a particle, body and multi-body systems. Students will solve problems of systems of rigid bodies using dynamic laws and Lagrange's equations. Students will solve a simple linear oscillation system.
Prerequisites:
Solving linear equations. Trigonometry and analytic geometry. Differentiation and integration of one variable. Vector algebra. Vector representation of forces and moments. Free body diagrams. Solving homogeneous and general the 2nd order linear differential equations.
Course contents:
The course “Dynamics” makes the students acquaint with basic axioms, laws and principles of theoretical and applied mechanics. Gradually students go over the following areas of dynamics: basic axioms, general dynamics of a particle, dynamics of a system of particles, dynamics of rigid bodies, moments and products of inertia of rigid bodies, dynamics of a system of rigid bodies (planar models), fundamentals of analytical dynamics (Lagrange’s Equations), linear vibration of systems (free, damped and forced vibrations with one degrees of freedom).
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:

The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 10 ECTS points out of 20 must be gained). The points gained in seminar tests are included in the final course evaluation.

Final examination: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. The first part of the examination is theoretical test which covers the topic discussed during whole seminars and lectures (maximum 40 ECTS points can be achieved). The second part is numeric solution of two practical problems form dynamics (maximum 40 ECTS points can be achieved).

Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and supplied by a theoretical question, proof, etc. The lecturer will specify exact demands like the number and types problems during the semester preceding the examination.
Final evaluation of the course is obtained as the sum of ECTS points gained in seminars and at the examination. To pass the course, at least 50 points must be reached.
Controlled participation in lessons:
Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.
Type of course unit:
    Lecture  13 × 2 hrs. optionally                  
    Exercise  6 × 2 hrs. compulsory                  
    Computer-assisted exercise  7 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

Dynamics of a mass point and system of mass points


Mass body(ies) geometry and dynamics of mass body and


Dynamics of system of mass bodies, multi-body systems applications


Introduction to analytical mechanics


Single degree of freedom system oscilations


Oscillation of dynamic systems with N DOF
    Exercise

Motion equations of a mass point


Motion equations of a system of maspoints


Dynamics of system of mass bodies


Methods of solving a movement of system of mass bodies (Newton's method, Lagrange’s equation of motion, etc.)



Excited oscillation of system with one degree of freedom
    Computer-assisted exercise

Motion equations of a mass point


Motion equations of a system of maspoints


Dynamics of system of mass bodies


Methods of solving a movement of system of mass bodies (Newton's method, Lagrange’s equation of motion, etc.)



Excited oscillation of system with one degree of freedom
Literature - fundamental:
1. Meirovitch, L.: Elements of Vibration Analysis, 2005
2. Slavík J.,Stejskal V.,Zeman V.: Základy dynamiky strojů, 2000
3. Harris V.,M., Crede Ch.: Shock and Vibration Handbook, 2005
Literature - recommended:
1. Slavík J.,Kratochvíl C.: Dynamika, 2005
2. Brousil J.,Slavík J.,Zeman V. : Dynamika, 2002
3. Beer F.,Johnston E.: Vector mechanics for Engineers. Dynamics, 2001
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-STI-A full-time study --- no specialisation -- Cr,Ex 5 Compulsory 1 3 W
B-STI-Z visiting student --- no specialisation -- Cr,Ex 5 Recommended course 1 1 W