Dynamics of structures 2

Garant předmětu:

Jiří Máca

Lecturer:

Jiří Máca

Tutor:

Jiří Máca, Karel Pohl

Supervisor:

Department of Mechanics

Synopsis:

Methods for solving natural and forced vibrations of building structures using the finite element method. Response to wind, earthquake, traffic. Interaction of structure and subsoil

Requirements:

Syllabus of lectures:

1. Basic principles of dynamics.

2. Finite element method in dynamics of structures - basic principles.

3. Finite element method in structural dynamics - formulation of the mass matrix.

4. Methods of solving natural vibrations using FEM - Rayleigh-Ritz, Jacobi.

5. Methods of solution of natural oscillations using FEM - Barn, subspace iteration.

6. Methods of solving forced oscillations using FEM - decomposition into eigenmodes.

7. Methods of solving forced oscillation using FEM - steady oscillation.

8. Methods of solving forced oscillations using FEM - direct integration.

9. Seismic loading of structures.

10. Calculation of seismic response of structures.

11. Response to wind loads.

12. Interaction between structure and subsoil.

13. Loading of transport structures - bridges and footbridges

Syllabus of tutorials:

1. Oscillations of systems with n degrees of freedom - proper oscillations, numerical methods (energy method, method of successive approximations, Gram-Schimdt orthogonalization).

2. Oscillations of systems with n degrees of freedom - free oscillations, development into natural oscillation shapes, influence of damping on the response of structures.

3. Oscillations of systems with n degrees of freedom - forced oscillations, numerical methods - Method of central differences.

4. Oscillations of systems with n degrees of freedom - forced oscillations, numerical methods - Newmark integration method, application to the development into eigenvibration shapes.

5. Oscillations of systems with n degrees of freedom - seismic loading of structures, calculation of response by direct integration of equations of motion to a given accelerogram.

6. Oscillations of systems with n degrees of freedom - seismic loading of structures, response solution using response spectrum, SRSS method. Test information.

Study Objective:

Students will have an overview of the main methods for solving natural and forced vibrations of building structures using the finite element method.

Study materials:

Máca J., Kruis J., Krejčí T.: Dynamika stavebních konstrukcí, ČVUT v Praze, 2018, ISBN 978-80-01-05719-3

Bittnar,Z.- Šejnoha,J.: Numerické metody mechaniky,Vydavatelství ČVUT, 1992

Humar J.: Dynamics of Structures, CRC Press/Balkema, 2012, ISBN 978-0-145-62086-4

Sokol M., Tvrdá K.: Dynamika stavebných konštrukcií, STU Bratislava 2011, ISBN 978-80-227-3587-2

Máca J.: Dynamika stavebních konstrukcí 2, ČVUT v Praze, 2021, https://mech.fsv.cvut.cz/web/

Note:

Further information:

https://mech.fsv.cvut.cz/cgi-bin/homeworks/student/student-identification?course=DY02

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• obor Konstrukce a dopravní stavby, zaměření Inženýrské konstrukce (compulsory course of the branch)
• Stavební Inženýrství - konstrukce a dopravní stavby, specializace Inženýrské konstrukce (PS)