The development of a wavelet-based nondestructive method for damage detection in structures that is effective and accurate is presented in this thesis. The proposed method is based on the analysis of the response signal of damaged structures subjected to various loading conditions. Although in practical applications, it will be required to experimentally measure the signals coming from the damaged structures, in this thesis the proposed method is validated through a numerical simulation using analytical models. Therefore, different approaches for modeling of cracked structures are considered: the Finite Difference method, the Strain Energy method, and the Finite Element method. The specific damaged structures chosen for this study are beams with different support conditions and plane frame. Continuous and discrete wavelet transforms are applied to perform the analysis of the damaged structure response. The main idea is to extract and to interpret the damage information from the coefficients of the wavelets of the signals coming from the measured structural response.; Numerical algorithms written in MATLAB are first developed to calculate the natural frequencies, modes of vibration and response of the undamaged structures subjected to static and dynamic loads. The cracks, which are modeled using the three approaches mentioned before, are then incorporated into the computer programs and frequency analyses are performed in order to select the most appropriate crack model for the next phase of the study. Next, a numerical simulation of the static and dynamic response of damaged structures is performed. Two wavelet transforms are applied to the response signals to extract damage information. The analysis, which is based on the signal processing theory, is also implemented in MATLAB.; The numerical studies show that wavelet analysis is capable of revealing small perturbations in the response signal induced by the presence of damage. The results prove that the discontinuity in the response signal can be easily detected only by using optimal selected wavelets. A peak on the wavelet coefficients plot in the space domain clearly shows the exact location of crack. Based on the obtained simulation results, it appears that this new method can provide an advantageous alternative to classical methods for structural damage detection, such as Fourier transform and modal analysis.
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