The detection of damage and changes in elastic properties of structures, using the variation of dynamic parameters, has been the subject of special attention for several years in the fields of mechanical and civil engineering. The general principle is based on the fact that the variation of physical properties (e.g. stiffness, mass, Young's modulus, boundary conditions) leads to a change in the dynamic characteristics of structures (e.g. resonance frequencies, modal damping and mode shapes). The presence of damage causes a decrease in the rigidity of structures, which give rise to an increase in flexibility and damping, which can be seen in mode shapes and frequency values. Using the change of this information between a healthy and damaged condition, several non-destructive methods have been proposed in the literature in order to identify and locate the damage. These practices and activities are of considerable importance. They allow us to anticipate and avoid breaks in structures, which are always catastrophic, and more generally, they allow us to establish the plans of a predictive maintenance, along with monitoring of the long-term of integrity (Structural Health monitoring). These monitoring methods are equally us popular because of the low cost of instrumentation, related to the appearance of new equipment at low cost, having the satisfactory performance. The objective of this work is to test different solutions, allow for detection, localization and quantification of changes in simple structures. Several methods have been tested and a new approach is proposed based on the use of the perturbation method. Three approaches are followed: finite element modeling (modal analysis), finite element numerical simulation (temporal analysis), and finally, experimental analysis of a Plexiglas beam in the laboratory. These three scopes of work have allowed us to test the sensitivity of global and local non-destructive methods (NDE) for detection and localization of damage. Changes associated with a local variation of Young's modulus (E) are tested numerically in modal and temporal analysis, and shown experimentally in local heating on the sections of beam. In all cases, we are in real life situations, where we identify modal characteristics by operational methods (Operative Modal Analysis) such as the random decrement technique and the method of decomposition in the frequency domain (Frequency Domain Decomposition). The results show a very good correlation between the numerical and experimental values obtained: resonant frequencies and mode shapes. For identifying damage, localization methods based on the curvature of mode shape, flexibility matrix, curvature of flexibility, and finally on the method of inversion of modes are employed. According to the results, the method of inversion proves effective in the case where modal variation is low and transient, whereas, the curvature of flexibility (ULS method) usually gives good results and appears robust when the changes are more pronounced.
