Course detail

Dynamics

FSI-5DTAcad. year: 2007/2008

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

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Karel Přikryl, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

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

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Assessment methods
The course-unit credit is granted under the condition of:
Active participation in seminars, good results in seminar tests of basic knowledge (three written tests during semester are recommended), solution of additional tasks in case of longer justified absence. Seminar tutor will specify these conditions in the first week of a semester.
Final evaluation is based on the result of examination, which has a combined form: written part (test of elementary knowledge + computational tasks) and oral part (discussion on written part with supplementary questions). It is necessary to have at least 50% of points in the test to pass the introductory part of the exam. The solution of 2-3 computational tasks follows then, the tasks come from typical profile areas of given subject. One of them can be supplied by theoretical question, proof, etc. The result of each task is evaluated from A (excellent) to F(failed). To pass the exam, only one task of all can be evaluated by F(failed), at the most.

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 is required. One absence can be compensated by attending a seminar with another group in the same week, or by elaboration of substitute tasks. Longer absence is compensated by special tasks according to instructions of the tutor.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme B2341-3 Bachelor's

    branch B2339-00 , 3. year of study, winter semester, compulsory

  • Programme N2301-2 Master's

    branch N2370-BS , 1. year of study, winter semester, compulsory

  • Programme N2301-3 Master's

    branch N2300-00 , 1. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Ing. Lubomír Houfek, Ph.D.
prof. Ing. Eduard Malenovský, DrSc.
doc. RNDr. Karel Pellant, CSc.

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

26 hours, compulsory

Teacher / Lecturer

Ing. Daniel Dušek, Ph.D.
doc. RNDr. Karel Pellant, CSc.
Ing. Pavel Švancara, Ph.D.
Ing. Pavel Zezula

Syllabus

1. Setting up equations of motion of a particle.
2. Solving of motion of a particle.
3. Dynamics of systems of particles, method of release, impulse theorems.
4. Moments and products of inertia.
5. Translational and rotational movement of rigid bodies.
6. General plane motion of rigid bodies. Rotation about a fixed point.
7. Effects of rotation of rigid bodies on the bearings.
8. System of constrained rigid bodies.
9. Lagrange’s equation of motion.
10. Linear vibrations. Single degree of a freedom system.
11. Forced vibrations. Single degree of a freedom system.
12. System vibration with two degree of freedom.
13. Revision lesson summarising the given lectures.