Structural analysis for dynamic loads

General Foundation

Students will become familiar with the basic concepts behind problems in structural dynamics and develop skills for managing the effects of time-dependent external loads in buildings and bridges. Furthermore, students will gain an understanding of the basic nature of the behavior of structures to transient loads. They will also gain in basic knowledge on the use of the finite element method for the analysis of structures to transient loads. Next, they will gain experience on the numerical simulation and computation of structural response under dynamic loading, along with an interpretation of the results. This will include the ability to use recorded time histories for structural identification purposes. Finally, they will be informed on the use of existing seismic design codes.

Structural response to transient loadings. Dynamic analysis of structures. Mathematical models. Numerical methods of dynamic response. Signal theory. Identification of the dynamic characteristics of structures. More details: Basic concepts in the dynamic analysis of structures. Equation of motion of Single Degree of Freedom (SDoF) systems. Free and forced vibrations. Damping in dynamic systems. Harmonic vibrations. Elastoplastic systems. Vibrations due to impact. Seismic ground motions. Response spectra. General principles of seismic analysis and design according to the EC8 seismic code. Use of the special purpose, web-based structural dynamics software program Dynasoft (http://dynasoft.civil.auth.gr). Numerical examples regarding the dynamic response analysis of SDoF systems. Ground motions as displacement versus time functions. Calculation of stress and displacements in SDoF systems as time functions. Free and forced vibration analysis using numerical methods. Numerical algorithms for SDoF systems. The Newmark-beta and the Wilson-theta algorithms: Theoretical background and numerical implementation. Others categories of numerical methods. Multi Degree of Freedom system (MDoF). Introduction to the Finite Element Method (FEM) used in representing MDoF systems. Modal analysis: Derivation of eigenfrequencies, modal damping ratios and mode shapes. The response spectrum analysis for MDoF systems. Numerical integration of MDoF systems under transient loads. Response history analysis. Numerical examples using FEM software. Continuous dynamic systems. The frequency domain and the Fourier transform. Numerical examples. Soil-structure-interaction problems. Static condensation techniques. Nonlinear dynamic analysis. Presentation of the ΕΝ 1998-3 Eurocode. Random vibrations and measurements. The Fast Fourier Transform (FFT). Derivation of the auto-correlation and cross-correlation functions for SDoF and MDoF systems. Signal processing: Use of filters, removal of noise and sign composition. Periodic and random signals. Sampling techniques. Digital signals. The Nyquist frequency. Signal properties: Correlated and uncorrelated signals and the correlation factor. Power and energy content of signals. The influence of noise. Fourier analysis of signals. The power spectral density function and the autocorrelation function. The amplitude spectrum and the phase spectrum of a signal. The use of filters in signal processing. The Parseval and the Wiener-Khintchine theorems. Signal representation in the time and in the frequency domains. The autocorrelation and cross-correlation functions for random signals. Identification of the dynamic characteristics of structures from ambient vibration data. Structural health monitoring issues.

30-11-2023