Keywords: structural damage, vibration, wave propagation, damage influence, flexibility matrix, parametric identification.

The damage influence on the vibrational behavior and on the wave propagation issues of a slender Euler-Bernoulli beam is investigated. In the vibration framework, the damage is assessed by considering changes in the reduced flexibility matrix of the structure. In the wave propagation framework, the presence of damage is perceived by an early echo output. A slender aluminium beam with an imposed damage scenario is considered for the numerical analysis. Both approaches showed a sensitivity to damage that enables these two techniques to be applied for damage identification purposes. Many vibration based damage identification approaches presented in the literature are built on the general framework of the finite element model (FEM) updating methods. These methods are intended to identify structural damage through determining changes in some parameters of a FEM of the structure. Hence, the damage identification problem may be cast as a minimization one and a set of parameters are sought in order to minimize an error function. This error is defined as the difference between some matrices of the FEM of the undamaged structure and the corresponding ones obtained from a modal testing of the damage structure. The basic idea of these approaches is that the modal properties (frequencies, mode-shapes and modal damping) are functions of the physical properties of the structure (mass, stiffness and damping) and changes in the physical properties due to damage will be reflected in the modal characteristics, which can be measured and used to infer about the damage. Damage identification can be also seen from the point of view of the wave propagation approach. Although this approach is much more uncommon in the literature than the vibration one, it has the advantage of being a fast technique of good accuracy. Some applications are reported in the fields of geophysics, medical ultrasonics, and non-destructive tests. The main goal of this research is to develop damage identification techniques based on the two approaches and compare them in terms of practice, accuracy and robustness. Initially, a simple damage imposed on an Euler-Bernoulli slender beam will be considered. Although having the inverse problem in mind, the concern here is to comparatively solve the analysis problem and study the sensitivity of each method to structural damage. Some numerical results showing the error with regard to a homogeneous beam response introduced by a damage, using both techniques, are reported. In a companion paper, the damage assessment using combined (hybrid) identification techniques for the vibration and wave propagation approaches is discussed.

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