Course detail

Engineering Mechanics

CESA-SDTMAcad. year: 2023/2024

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)

Entry knowledge

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.

Rules for evaluation and completion of the course

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.
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 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.
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.

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.
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.

Study aids

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)
Hibbeler R.C.: Engineering Mechanics-Statics and Dynamics, 2001 (EN)

Recommended reading

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

eLearning

eLearning: currently opened course

Classification of course in study plans

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

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

Ing. Jiří Majzner, Ph.D.

Syllabus

1. Kinematics of a point - rectilinear and curvilinear motion, circular motion and harmonic motion. 2. Kinematics of translational and rotational motion of a rigid body, kinematics of general planar motion of a body, solution of bodies acting GPM in mechanisms. 3. Kinematics of compound point motion of bodies, kinematic solutions of mechanisms. 4. Simultaneous rotations, kinematics of spherical motion. 5. Dynamics of a mass point, dynamics of a system of mass points. 6. Equations of motion of a rigid body in translational, rotational motion. 7. Moments of inertia of solids. Balancing of rigid rotors. 8. Dynamics of general plane motion and spherical motion of a solid. Gyroscopic moment. 9. Dynamics of a system of bound bodies - the plane case. Construction of equations of motion of release from the system. 10. Dynamics of a system of bound bodies - solution by methods of analytical mechanics. Lagrange's equations of the second kind. 11. Free vibration of a system with one degree of freedom. Forced oscillations of a system with one degree of freedom. Kinematic excitation. 12. Linear and nonlinear dynamical systems. 13. Experimental dynamics. 

Fundamentals seminar

14 hours, compulsory

Teacher / Lecturer

Ing. Jiří Majzner, Ph.D.

Syllabus

1. Kinematics of general plane motion of a body. Determination of the velocity pole. Determination of velocity and acceleration of individual points of a body.
2. Kinematics of the compound motion of a point of a body in mechanisms.
3. Dynamics of a mass point and a system of mass points. Application of basic theorems of dynamics.
4. Dynamics of plane systems of bodies - construction of equations of motion by the method of relaxation.
5. Dynamics of plane systems of bodies - construction of equations of motion by methods of analytical mechanics.
6. Equation of motion for an oscillating system with one degree of freedom. Damped and undamped free oscillations.  

Computer-assisted exercise

12 hours, compulsory

Teacher / Lecturer

Ing. Jiří Majzner, Ph.D.

Syllabus

1. Kinematics of a point - rectilinear and curvilinear motion. Determination of trajectory, velocity and acceleration. Kinematics of translational and rotational motion of bodies.
2. Kinematics of mechanisms. 
3. Dynamics of bodies. Equations of motion.
4. Moments of inertia.
5. Dynamics of rotational and general plane motion of a body.
6. Dynamics of planar systems of bodies with one degree of freedom.
7. Solution of the linear equation of motion of oscillation.  

eLearning

eLearning: currently opened course