1. Assessment of civil engineering structures subjected by dynamic loads. 2. Foundations the theory vibration of civil engineering structures. Models with single degree of freedom system (SDOF). 3. Free Vibration. Response SDOF systems to specials form of excitation. Damping models. 4. Measurement of frequencies and damping. Response of SDOF to general type of action. 5. Numerical analysis of SDOF response. Frequency analysis. FFT. 6. Continuous computational models – tension and bending of beam. Modal analysis. Vibration of plates. 7. Newton law application. Hamilton principle. 8. Multi degree of freedom models. Lagrange equations. 9. Discrete and continuous models. Modal analysis of two degree of freedom models. 10. Response solution using mode superposition method. Rayleigh method. 11. Natural frequency and eigenvalue vectors characteristics. Rayleigh-Ritz method. General eigenvalues problem. 12. Dynamic analysis by finite element method (FEM). Element matrices. The global system of equations Systems matrices. Modal analysis. Direct integration equations of motion. 13. Response solution structures on seismic loads.

1. Calculation of equivalent stiffness and mass of models with single degree of freedom system (SDOF) 2. Derivation of equation of motion of SDOF systems 3. Free vibration of undamped SDOF system – calculation of natural frequencies 4. Free vibration of undamped SDOF system – calculation of damping parameters 5. Response of SDOF system to harmonic excitation 6. Response of SDOF system to various type excitations (impulse, constant force etc.) 7. Calculation of frequencies and modes of vibrations of continuous systems – rods and plates 8. Derivation of equation of motion system with 2DOF (translational and rotational motion) 9. Assembly equation of 2DOF systems to calculate the frequencies and modes of vibrations and their solution 10. Assembly modal matrices. Using procedures for normalizing mode of vibration and plotting modes. 11. Solution by mode-superposition method of the 2DOF system to harmonic excitation. 12. Tuning dampers for vibration reduction simple systems. 13. Derive elastic response spectra for solutions to seismic excitation.