Course detail

DYNAMICS

FAST-5D8Acad. year: 2021/2022

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

2

Guarantor

doc. Ing. Vlastislav Salajka, CSc.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

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

Not applicable.

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

ANSYS 5.6 Theory Reference ANSYS Inc.. Canonsburg, Pa, October 22 1999
Craig, R. R. Jr.: Structural Dynamic. John Wiley & Sons, Inc. 1981
Inman, J. D.: Engineering Vibration. Prentice-Hall Internacional Inc. 1994

Recommended reading

Not applicable.

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.

Exercise

13 hours, compulsory

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.