Dynamics and Stability of Structure

Lecturer:

Tutor:

Supervisor:

Department of Mechanics

Synopsis:

Mechanical vibrations of particles - free

and forced vibrations, steady-state vibration, damped

vibrations. Multiple degree-of-freedom systems. Harmonic

vibration of foundations. Impact loading. Wind and seismic

effects.Linear stability of structures - initial stress matrix,

critical value of loading . Frame imperfections, second order

theory.Principle of virtual work in dynamic problems,

consistent and lumped mass matrix.Static condensation.

Eigenvalue analysis - Rayleigh-Ritz method, inverse iteration,

Jacobi method, subspace iteration method, Lanczos method.

Dynamic response analysis - mode superposition analysis, direct

integration methods, response spectrum method. Response to

harmonic excitation. Introduction to geometrically nonlinear

finite element analysis - tangent stiffness matrix, residual

out-of-balance forces. Incremental-iterative solutions, Newton-

Raphson method.

Requirements:

none

Syllabus of lectures:

1. Mechanical vibrations of particles - free and forced vibrations

2. Steady-state vibration, damped vibrations

3. Multiple degree-of-freedom systems

4. Harmonic vibration of foundations

5. Impact loading, wind and seismic effects

6. Linear stability of structures - initial stress matrix, critical value of loading

7. Frame imperfections, second order theory

8. Principle of virtual work in dynamic problems, consistent and lumped mass matrix

9. FEM - eigenvalue analysis

10. FEM - dynamic response analysis

11. FEM - response to harmonic excitation

12. Introduction to geometrically nonlinear finite element analysis

13. Incremental-iterative solutions

14. Tests

Syllabus of tutorials:

Study Objective:

Students will be able to solve free and forced vibrations, damped vibrations of structures, wind and seismic effects. They will be introduced to linear stability of structures and dynamic response analysis.

Study materials:

1. Clough, R.W. and Penzien, J. (1993) Dynamics of structures. McGraw-Hill., 2. Bittnar, Z. and Šejnoha, J. (1996) Numerical methods in structural engineering. ASCE Press.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: