Course detail

Computer Methods in Dynamics

FSI-RPMAcad. year: 2019/2020

The course is focused on the dynamics of mechanical systems. The lectures deal with several basic areas, such as oscillation of one and multi-degrees of freedom mechanical systems, on oscillation of flexible body, nonlinear systems and multi-body systems. The mentioned tasks will be explained in seminars, and numerical methods will be used to solve the dynamic problems.

Learning outcomes of the course unit

The students will have detailed knowledge of vibration of systems with single and several degrees of freedom. They will be able to calculate eigenfrequencies and responses of these systems with different types of excitation. They will be able to solve practical problems that can be modeled in this way. The student will have knowledge of the vibration of basic continuum bodies. They will be able to create models using finite element method and multi-body systems. The students will be able to apply the basic methods of linearization in the solution of nonlinear systems vibration.


Students are expected to have the following knowledge: linear algebra, differentiation, integration, solution of differential equations, matrix arithmetic, basic programming, particular mathematical software (MATLAB), basic statistics, elasticity, fundamental principles of dynamics, formation of kinetic equations of plane motion and solution of free oscillating systems with one degree of freedom.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Meirovitch,L.: Elements of Vibration Analysis, 2002
William T. Thomson, Theory of Vibration With Applications 5th Edition (EN)
Crede,Ch.,Harris,C.: Shock and Vibration Handbook, 2005
Slavík,J.,Stejskal,V.,Zeman,V.: Základy dynamiky strojů, ČVUT Praha, 2000.
Harris,C., Piersol, A., G.: Shock and Vibration Handbook, McGRAW-HILL New York, 2002.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Seminars are focused on practical topics.

Assesment methods and criteria linked to learning outcomes

The course-unit credit is granted under the condition of active participation in seminars and gain at least 20 points of 40. The points can be obtained by elaboration of partial tasks and presentations. The gained points from the exercise is part of the final classification of the subject.
Final examination: The exam is divided into two parts. The evaluation of the exam is based on the classifications of each part. If one of the parts is graded F, the final grade of the exam is F. The content of the first part is a test, of which a maximum of 30 points can be obtained. The content of the second part is a solution of typical problems. It is possible to gain up to 30 points from this part. The form of the exam, types, number of examples or questions and details of the evaluation will be given by the lecturer during the semester.
The final evaluation is given by the sum of the points gained from the exercises and exam. To successfully complete the course, it is necessary to obtain at least 50 points, where the maximum of 100 ECTS points can be reached.

Language of instruction


Work placements

Not applicable.


The aim of the course is to learn about linear and non-linear vibrations of one and multi degrees of freedom mechanical systems, follows with vibration of continuum, basic methods of motion equation solving process and with dynamics of multi-body systems.

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

Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. One absence can be compensated for by elaboration of substitute tasks.

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-IMB , 1. year of study, winter semester, 5 credits, compulsory
    branch M-MET , 1. year of study, winter semester, 5 credits, compulsory

Type of course unit



26 hours, optionally

Teacher / Lecturer


1. Introduction to computer methods of dynamics
2. Free oscillation of one degree of freedom oscillator, eigenvalue problem
3. Excitation of one degree of freedom oscillator
4. Oscillation of multi-degrees of freedom dynamic system
5. Computational methods of solving eigenvalues problem and methods of motion equation integration
6. Vibrations of nonlinear system
7. Method for reducing size of dynamic model
8. Longitude and torsional oscillation of beam
9. Transversal oscillation of beam
10. Oscillation of rectangular and circular plates and membranes
11. Multi-body systems
12. Models of dynamic systems
13. Examples of practical problems

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


1. Solving of motion equation
2. Free oscillation of one degree of freedom system
3. Excitation of one degree of freedom system
4. Solving of motion equations of the multi degrees of freedom systems
5. Methods of solving eigenvalues problem and methods of motion equation integration
6. Nonlinear systems
7. Methods for reducing the size of dynamic model
8. Oscillation of beam (longitude and torsional)
9. Oscillation of beam (transversal)
10. Oscillation of rectangular and circular plates and membranes
11. Multi-body system
12. Multi-body system
13. Multi-body system and flexible bodies