Course detail

Engineering Mechanics

FSI-DTMAcad. year: 2015/2016

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

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Krejsa, Ph.D.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics (ÚMTMB)

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 3 seminar tests of basic knowledge (at least 15 ECTS points out of 30 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 70 ECTS points can be reached. Solution of several computational problems is demanded. The problems come from typical profile areas of given subject and can be 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 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 and activity in the seminars are required. One absence can be compensated by attending a seminar with another group in the same week, or by elaboration of substitute tasks. The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 15 ECTS points out of 30 must be gained). The points gained in seminar tests are included in the final course evaluation.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Brát V.,Rosenberg J.,Jáč V.: Kinematika, 2005 (CS)
Juliš K.,Brepta R. a kol.: Mechanika II.díl-Dynamika,2002 (CS)

Type of course unit

Lecture

52 hod., optionally

Teacher / Lecturer

doc. Ing. Zdeněk Hadaš, Ph.D.

Syllabus

Lectures:
1. Kinematics of a particle - rectilinear and curvilinear motion. Harmonic motion.
2. Kinematics of a body - translational, rotational and planar motion. Planar kinematics of rigid bodies in a mechanism.
3. Planar kinematics of rigid bodies - combined motion.
4. Kinematics motion analysis of mechanisms. Spherical motion.
5. Dynamics of particle. Dynamics of a system of particles.
6. Motion equations of rigid bodies - translation, rotational and planar motion. Inertia moments. Balancing of rotors.
7. Dynamics of spherical motion. Gyroscopes.
8. Dynamics of planar multi body systems. Motion equations based on Newton's Law.
9. Dynamics of planar multi body systems. Lagrangian mechanics, D'Alembert's principle and generalized forces and Hamilton's principle.
10. Dynamics of multi body system with flexible parts. Stability. Oscillation with 1 DOF.
11. Excited oscillation with 1 DOF.
12. Non-linear dynamics.
13. Excited oscillation of resonance system with several DOF. Dynamics of flexible bodies.

Exercise

14 hod., compulsory

Teacher / Lecturer

Ing. Luděk Janák
Ing. Jan Smilek, Ph.D.
Ing. Petr Marcián, Ph.D.
doc. Ing. Zdeněk Hadaš, Ph.D.
Ing. Pavel Švancara, Ph.D.

Syllabus

Seminars C1:
1. Kinematics of a particle - rectilinear and curvilinear motion. Trajectory, velocity and acceleration.
2. Kinematics of planar rigid body motion - Graphical analysis. Instantaneous centre of zero velocity.
3. Kinematics of planar mechanisms - Graphical analysis of combined motion.
4. Dynamics of particle. Dynamics of a system of particles. Laws of conservation.
5. Motion equations of rigid body motion.
6. Dynamics of planar multi body systems - motion equations.
7. Excited oscillations. Analysis of a resonance system with 1 DOF.

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Krejsa, Ph.D.

Syllabus

Seminars C2A:
1. Kinematics of planar mechanisms. Numerical analysis.
2. Kinematics of planar mechanisms. Multi body system.
3. Inertia moments.
4. Dynamics of planar multi body systems.
5. Motion equation of a resonance system with 1 DOF.
6. Dynamics of a resonance system with 1 DOF.

VUT

Faculties

University Institutes

Parts

Engineering Mechanics

Type of course unit