Course detail


FAST-CD05Acad. year: 2020/2021

Assessment of civil engineering structures subjected to dynamic loads. Vibration theory fundamentals. Free vibration of single degree of freedom systems (SDOF). Experimental determination of fundamental natural frequency and damping factor. Response of SDOF systems to harmonic excitation. Response of SDOF systems to special forms of excitation and to general dynamic excitation. Frequency domain analysis. DFT, FFT. Mathematical models of continuous systems - axial and transverse vibration of elastic beams. Vibration of thin flat plate. Mathematical models of multi degree of freedoms (MDOF) systems. Application of Newton’s Laws to lumped-parameter models. Hamilton’s principle. Lagrange’s equations. Application of Lagrange’s equations to continuous systems. Free vibration of MDOF systems. Dynamic response by mode superposition method. The eigenvalue problem and numerical evaluation of modes and frequencies of MDOF systems. Dynamic analysis by finite element method (FEM). Element stiffness, damping, mass matrices and element force vector. Assembly of system Matrices. Vibration analysis employing FEM models. Direct integration methods for dynamic response. Response of systems to seismic excitation.


Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

The course output is knowledge in the theory of structure vibration area. Student knows necessary technicals and became acquainted with option of computational models useful for dynamic analyses of the structure. The skills are possible to apply in solving of dynamic response of the structure. Obtained knowledge and acquirements are the basis for practical design and appreciation of dynamically loaded structures. The theoretic knowledge is instrumental towards to understanding of single type of dynamic analyses implemented in modern computational programs based on FEM.


Diagrams of internal forces on a beam, the meaning of the quantities: stress, strain and displacement, Hook’s law, equilibrium conditions for a beam, physical and geometrical equations for a beam, foundations of higher mathematics, variational principles, theory of plates, theory of FEM,.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Craig, R. R., Jr.: Structural Dynamics. John Wiley & Sons, Inc., 1981. (EN)
Inman, J.D.: Enginnering Vibration. Prentice-Hall International, 1994. (EN)
Koloušek, V.: Dynamika stavebních konstrukcí I. SNTL - Nakladatelství technické literatury, Praha, 1967. (CS)
Baťa, M., Plachý, V.: Vyšetřování dynamických účinků na stavební konstrukce. SNTL – Nakladatelství technické literatury, Praha, 1978. (CS)
Bittnar, Z., Šejnoha, J.: Numerické metody mechaniky. Vydavatelství ČVUT, Praha, 1992. (CS)

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Assessment of civil engineering structures subjected by dynamic loads.
2. Foundations the theory vibration of civil engineering structures. Models with single degree of freedom system (SDOF).
3. Free Vibration. Response SDOF systems to specials form of excitation. Damping models.
4. Measurement of frequencies and damping. Response of SDOF to general type of action.
5. Numerical analysis of SDOF response. Frequency analysis. FFT.
6. Continuous computational models – tension and bending of beam. Modal analysis. Vibration of plates.
7. Newton law application. Hamilton principle.
8. Multi degree of freedom models. Lagrange equations.
9. Discrete and continuous models. Modal analysis of two degree of freedom models.
10. Response solution using mode superposition method. Rayleigh method.
11. Natural frequency and eigenvalue vectors characteristics. Rayleigh-Ritz method. General eigenvalues problem.
12. Dynamic analysis by finite element method (FEM). Element matrices. The global system of equations Systems matrices. Modal analysis. Direct integration equations of motion.
13. Response solution structures on seismic loads.


To get knowledge from the structure vibration theory, acquire appropriate terminology, recognize advantages of the alternatives to the dynamic analysis models, utilize up-to-date solving methods. Skills can be used as a basis for the real design of dynamically loaded structures; the theoretical knowledge helps to understand dynamic analyses implemented in modern computational programs based on FEM.

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Type of course unit



26 hours, optionally

Teacher / Lecturer


26 hours, compulsory

Teacher / Lecturer