Course detail

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.

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.

High level of mathematics, fundamentals of physics, theory of mechanics and elasticity.

Examination of the response of structures subjected to excitation. Bases of the vibration theory. Free vibration and general dynamic excitation on single degree-of-freedom models. Methods for determining the damping factor. Frequency domain analysis. DFT, FFT. Mathematical models of continuous systems - Axial and transverse vibration of elastic beams. Free vibration. Vibration of thin flat plate. Hamilton’s principle. Rayleigh’s method. Mathematical models of MDOF systems. Application of Newton’s Laws to lumped-parameter models. Lagrange’s equations. Application of Lagrange’s equations to continuous models. Free vibration of MDOF systems. Dynamic response by mode superposition method. The eigenvalue problem. FEM. Element stiffness and mass matrices. Modal analysis. Direct integration methods for dynamic response. Models of damping.

n. a.

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1.Examination of civil engineering structures loaded by dynamic effects.
2.Bases of the theory of civil engineering structures vibration. Single degree of freedom model.
3.Modal analysis. SDOF response on special action. Damping models.
4.Eigenvalue frequencies measurement. Response on general type of action.
5.Numerical analysis of SDOF response. Frequency analysis. FFT.
6.Continuous computational models – bended beam. Modal analysis. Vibration of plates.
7.Newton law application. Hamilton principle. Rayleigh method.
8.Models with finite degree of freedom. Lagrange equation.
9.Discrete and continuous models. Two degree of freedom model modal analysis.
10.Response solution using mode superposition. Rayleigh method.
11.Eigen frequency and eigen vectors characteristics. Rayleigh-Ritz method. Eigenvalues tasks – introduction.
12.Usage of FEM in dynamic analysis. Element matrix. Modal analysis.
13.Mode superposition method. Direct integration of motion equations.

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

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