Course detail

Dynamics

FAST-CD05Acad. year: 2010/2011

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.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Vlastislav Salajka, CSc.

Department

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.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

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

Course curriculum

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.

Work placements

Not applicable.

Aims

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Craig, R. R., Jr.: Structural Dynamics. John Wiley & Sons, Inc., 1981. (EN)
Inman, J.D.: Enginnering Vibration. Prentice-Hall International, 1994. (EN)

Recommended reading

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)

Classification of course in study plans

  • Programme N-P-C-SI Master's

    branch S , 1. year of study, summer semester, compulsory

  • Programme N-K-C-SI Master's

    branch S , 1. year of study, summer semester, compulsory

  • Programme N-P-E-SI Master's

    branch S , 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, obligation not entered

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.

Exercise

26 hours, obligation not entered

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.