A Novel VBSHM Strategy to Identify Geometrical Damage Properties Using Only Frequency Changes and Damage Library  
[PERSON]  
1 INSA Centre Val de Loire, Universite d'Orleans, Universite de Tours, Laboratoire de Mecanique Gabriel Lame EA 7494, 3 Rue de la Chocolaterie, F-41034 Blois, France; [EMAIL_ADDRESS] (A.D.); [EMAIL_ADDRESS] (V.D.) 20 October 202  
damage localization and estimation, using changes in natural frequencies for 1D and 2D structures and relying on a FE model of the structures. [PERSON] (2018) proposed Damage Location Assurance Criterion (DLAC) and after extended to the statistical correlation coefficient, which is called Multiple Damage Location Assurance Criterion (MDLAC) (2018). The two methods rely on changes in natural frequencies for estimating the position and size of defects in complex structures. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) developed a method for the estimation of damage using measured changes in the natural frequencies. They presented eigenvalues variation to localize damage using reductions in the stiffness by derived equations from the first-order perturbation. They have also introduced a criterion to solve these equations by minimizing the difference between eigenvalue problems for the undamaged and damaged structures. It was concluded that few frequencies allows the estimation and location of single or multiple defect in structures such as beams but that the results are sensitive to uncertainty on the natural frequencies. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) made a sensitivity analysis on a cracked beam and used a local modal crack sensitivity in order to localize damage using natural frequency measurement only. According to [PERSON] and [PERSON] (2018), [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) proposed a technique to detect the crack size and position using a so-called Frequency Shift Coefficient. [PERSON] et al. [PERSON] et al. (2018) use a model for stiffness reduction due to a crack and a minimization involving the sensitivity matrix from a Finite Element (FE) model and a set of five measured natural frequencies for finding crack depth and location on a cantilever beam. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) examined natural frequencies from the Rayleigh quotient for a clamped beam with an arbitrary number of cracks. The cracks are represented as spring stiffnesses. Through an iterative procedure, three experimentally measured frequencies of a beam with fixed ends are sufficient to locate cracks and estimate their severity using the explicit expression of the Rayleigh quotient. [PERSON] et al. [PERSON] et al. (2018) introduced a method based on the first-order analytical estimation of the variation of natural frequencies due to structural modifications. It allows, with the help of a minimization procedure, to quantify and localize several structural modifications i.e., damage on a Euler-Bernoulli beam subject to axial constraint, using only modal shapes of the intact structure and natural frequencies of both intact and modified structures. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) used normalized frequencies method for a specified damage location in the cantilever beam. The damaged zone is determined only by the classification of the normalized frequencies of the structure. The change in stiffness caused by the damage is reflected locally in the frequencies. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) have presented a theoretical and experimental study of a frequency-based damage detection method. The method uses the modal frequency curve of a beam with moving point mass and discrete wavelet transform in order to build a damage index. [PERSON] et al. (2018) used the link between natural frequency shift and modal curvature to localize and identify defects in a multispan beam. [PERSON] et al. [PERSON] et al. (2018) presented a study of relative natural frequency change curves for characterization of damage in a fixed-fixed beam. They detail the relationship between these curves and mode shapes.