Course detail

Dynamics

FSI-5DT-AAcad. year: 2016/2017

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 and n degrees of freedom).

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Eduard Malenovský, DrSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

Dynamics deals with kinetics, i.e. with the relationship between motions and forces. Students will be able to: Construct and analyze free body diagrams (FBD) and write equations of motion of this body. Solve problems of systems of rigid bodies altogether using work and energy and Lagrange’s equations. Analyze dynamic systems and recommend changes, as well as to analyze the effects of those changes. Solve simple linear vibration systems.

Prerequisites

Solving simultaneous linear a quadratic equations. Trigonometry and analytic geometry. Differentiation and integration of one variable. Vector algebra. Vector representation of forces and moments. Free body diagrams. Solving homogeneous 2nd order differential equations, and the general 2nd order linear differential equation.

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

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. 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.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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.

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

Attendance at seminars is required. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. One absence can be compensated for by attending a seminar with another group in the same week, or by elaboration of substitute tasks.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Harris V.,M., Crede Ch.: Shock and Vibration Handbook, 2005
Meirovitch, L.: Elements of Vibration Analysis, 2005
Slavík J.,Stejskal V.,Zeman V.: Základy dynamiky strojů, 2000

Recommended reading

Beer F.,Johnston E.: Vector mechanics for Engineers. Dynamics, 2001
Brousil J.,Slavík J.,Zeman V. : Dynamika, 2002
Slavík J.,Kratochvíl C.: Dynamika, 2005

Classification of course in study plans

  • Programme M2E-A Master's

    branch M-IND , 1 year of study, winter semester, elective (voluntary)

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Eduard Malenovský, DrSc.

Syllabus

1. Dynamics of a particle, relative motion of a particle.
2. Dynamics of systems of particles, moments and products of inertia.
3. Mechanics of rigid bodies, translational motion, rotation about fixed axis.
4. General plane motion.
5. Three-dimensional motion of a rigid body, rotation about fixed point, gyroscope.
6. System of constrained rigid bodies. Methods of solutions.
7. Introduction to analytical dynamics.
8. Lagrange's equations of motion.
9. Linear vibrations. Single-degree-of-freedom systems.
10.Forced vibrations of single-degree-of-freedom systems.
11.Kinematic excitation
12.Vibrations with two-degree-of-freedom.
13.Forced vibrations with two-degree-of-freedom.

Exercise

12 hod., compulsory

Teacher / Lecturer

Ing. Lukáš Březina, Ph.D.

Syllabus

1. Setting up equations of motion of a particle.
2. Dynamics of spherical motion.
3. Effects of rotation of rigid bodies on the bearings.
4. Lagrange’s equation of motion.
5. System vibration with two degree of freedom.
6. Revision lesson summarising the given lectures.

Computer-assisted exercise

14 hod., compulsory

Teacher / Lecturer

prof. Ing. Eduard Malenovský, DrSc.

Syllabus

1 Setting up equations of motion of a particle.
2. Dynamics of systems of particles, method of release, impulse theorems.
3. Moments and products of inertia.
4. Translational and rotational movement of rigid bodies.
5. General plane motion of rigid bodies. Rotation about a fixed point.
6. Linear vibrations. Single degree of a freedom system.
7. Forced vibrations. Single degree of a freedom system.