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This paper aims to establish a damage identification methodology, called the Frequencies' Ratio Surfaces Intersection method (FRSI-method), for predicting not only the location and depth of the crack but also the crack orientation in a circular cross section beam. Two new criterions %∆cracked i and %Ψcracked i, j that consider only the ratio of the natural frequencies of the cracked beam are introduced and discussed in order to detect the crack parameters. In order to avoid worse diagnostic, it is demonstrated that a robust identification of crack location is possible by investigating the emergence of extra antiresonance peaks on Frequency Response Functions. The size, location and orientation of the crack are identi- fied by finding the intersection of the surfaces that correspond to the natural frequencies' ratios of the lower vertical and horizontal modes. One of the advantages of the proposed approach is that, unlike other vibrationbased damage identification procedures, it does not use a priori accurate knowledge of the angular frequencies of the uncracked structure and its material properties. Only the Frequency Responses Functions and natural frequencies of the cracked structure are needed to identify the crack parameters (i.e. the non-dimensional crack depth, the crack location and the crack orientation). It is demonstrated that damage identification methodology, called the Frequencies' Ratio Surfaces Intersection method (FRSI-method), can be used for the detection of the crack size, location and orientation with satisfactory precision, even if noise level has been added to the simulations.

Damage Assessment Based on the Frequencies' Ratio Surfaces Intersection Method for the Identification of the Crack Depth, Location and Orientation