Course detail

Engineering Mechanics

CESA-SDTMAcad. year: 2019/2020

The course “Engineering mechanics” is subdivided into two branches: kinematics and dynamics. Kinematics is aimed at proper formulation of motion, i.e. the students have to be able to determine how to calculate trajectory and position of rigid body or a multi body system. Kinematics of a particle, planar kinematics and a three-dimensional rigid body motion are discussed in the introduction to the course. The graphical and numerical methods for solution of planar mechanism motion are treated. Step by step the students are led through the following areas of dynamics: basic axioms, general dynamics of a particle, dynamics of a system of particles, dynamics of rigid bodies, inertia moments of rigid bodies and dynamics of multi body systems. The fundamentals Newton's Laws are used for solving of practical tasks. The solving based on methods of analytical dynamics is presented too. Description, analysis and solving the fundamental characteristics of linear resonance system are treated.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Petr Sedlák, Ph.D.

Department

Department of Physics (UFYZ)

Learning outcomes of the course unit

The course will provide students with knowledge necessary to solve the kinematics and dynamics problems of planar multi body systems. Solve kinematics outputs as trajectory (position), velocity and acceleration of any point of the moving bodies, in terms of a fixed coordinate system, as well as in terms of moving coordinate systems. The students will be able analysed relation between actuated active force effects and kinematics of moving body.

Prerequisites

Vector and matrix. Resultants of a force and couple system. Further reduction of a force and couple system. Constraints for a rigid body. Model of rigid body with respect of Newton's Laws. DOF analysis. Equations of static equilibrium in two and three dimensions. Characteristics of a dry friction and rolling resistance. Coordinate systems. Centre of gravity. Definition of work and virtual work for variable force and for variable moment. Principle of work and energy. Conservation of energy theorem. Principle of linear impulse and momentum. Conservation of linear momentum and of angular momentum. Statement of Newton’s laws of motion. Basic terminology of planar kinematics - radius vector, velocity and acceleration. Curvilinear motion of particle-determination of tangential and normal component of acceleration.

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

1. Kinematics of a particle - rectilinear and curvilinear motion. Circular and harmonic motion.
2. Kinematics of a body - translational, rotational and planar motion. Planar kinematics of rigid body in a mechanism.
3. Kinematics motion analysis of mechanisms - combined motion.
4. Kinematics of a coupled rotation. Spherical motion.
5. Dynamics of a particle. Dynamics of a system of particles.
6. Motion equations of rigid bodies - translation, rotational and planar motion.
7. Inertia moments. Balancing of rotors.
8. Dynamics of planar and spherical motion. Gyroscopes.
9. Dynamics of planar multi body systems. Newton's Law.
10. Dynamics of planar multi body systems. Lagrangian mechanics.
11. Oscillation with 1 DOF. Excited oscillation with 1 DOF. Kinematic excitation.
12. Linear and non-linear dynamic systems.
13. Experimental dynamics.

Work placements

Not applicable.

Aims

The course “Engineering mechanics” provides the students with knowledge of basic axioms, laws and principles of classical mechanics. The emphasis is to make students understand the physical principles of rigid bodies motion and multi body systems and students will apply them to solve simple technical problems in practice.
Kinematics is based on formulation of trajectory, body motion, multi body systems and determination of kinematic quantities, position, velocity and acceleration. For simple mechanical systems, students learn to solve kinematics of mechanisms and analyse the velocity and acceleration of key points of multi body system.
Determination of the kinematic quantities is necessary for further dynamic solving. Dynamics is based on knowledge of solving multi body systems.

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

Brát V.,Rosenberg J.,Jáč V.: Kinematika, 2005 (CS)
Hibbeler R.C.: Engineering Mechanics-Statics and Dynamics, 2001 (EN)
Juliš K.,Brepta R. a kol.: Mechanika II.díl-Dynamika, 2002 (CS)

Recommended reading

C. Kratochvíl, E. Malenovský: Mechanika těles. Sbírka úloh z dynamiky, 2000 (CS)
Hibbeler R.C.: Engineering Mechanics-Statics and Dynamics, London 1995 (EN)
Přikryl K.: Kinematika, 2005 (CS)
Přikryl, K., Malenovský, E., Úlohy z kinematiky, 2005 (CS)
Slavík J.,Kratochvíl C.: Mechanika těles-Dynamika, 2000 (CS)

Classification of course in study plans

  • Programme SPC-STC Bachelor's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Petr Sedlák, Ph.D.

Syllabus

1. Kinematika bodu – přímočarý a křivočarý pohyb, pohyb po kružnici a harmonický pohyb.
2. Kinematika translačního a rotačního pohybu tuhého tělesa, kinematika obecného rovinného pohybu tělesa, řešení těles konající ORP v mechanismech.
3. Kinematika složeného pohybu bodu těles, kinematické řešení mechanismů.
4. Současné rotace, kinematika sférického pohybu.
5. Dynamika hmotného bodu, dynamika soustavy hmotných bodů.
6. Pohybové rovnice tuhého tělesa při translačním, rotačním pohybu.
7. Momenty setrvačnosti těles. Vyvažování tuhých rotorů.
8. Dynamika obecného rovinného pohybu a sférického pohybu tělesa. Gyroskopický moment.
9. Dynamika soustavy vázaných těles - rovinný případ. Konstrukce pohybových rovnic uvolňování ze soustavy.
10. Dynamika soustavy vázaných těles - řešení metodami analytické mechaniky. Lagrangeovy rovnice II.druhu.
11. Volné kmitání soustavy s jedním stupněm volnosti. Vynucené kmitání soustavy s jedním stupněm volnosti. Kinematické buzení.
12. Lineární a nelineární dynamické systémy.
13. Experimentální dynamika.

Fundamentals seminar

14 hod., compulsory

Teacher / Lecturer

Ing. Jiří Majzner, Ph.D.

Syllabus

1. Kinematika obecného rovinného pohybu tělesa. Určování pólu rychlosti. Určování rychlosti a zrychlení jednotlivých bodů tělesa.
2. Kiinematika složeného pohybu bodu tělesa v mechanismech.
3. Dynamika hmotného bodu a soustavy hmotných bodů. Aplikace základních vět dynamiky.
4. Dynamika rovinných soustav těles – konstrukce pohybových rovnic metodou uvolňování.
5. Dynamika rovinných soustav těles – konstrukce pohybových rovnic metodami analytické mechaniky.
6. Pohybová rovnice pro kmitající soustavu s jedním stupněm volnosti. Tlumené a netlumené volné kmity.

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Petr Sedlák, Ph.D.

Syllabus

1. Kinematika bodu - přímočarý a křivočarý pohyb. Určování dráhy, rychlosti a zrychlení. Kinematika translačního a rotačního pohybu těles.
2. Kinematika mechanismů.
3. Dynamika těles. Pohybová rovnice.
4. Momenty setrvačnosti.
5. Dynamika rotačního a obecného rovinného pohybu tělesa.
6. Dynamika rovinných soustav těles s jedním stupněm volnosti.
7. Řešení lineární pohybové rovnice kmitání.