PSI - Issue 68

Gomez-Mancilla Julio C. et al. / Procedia Structural Integrity 68 (2025) 318–324 Gomez-Mancilla J / Structural Integrity Procedia 00 (2025) 000–000

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4. Damage Characterization Nonlinear Method Method briefly exposed . The method is a non-linear analysis because, although the SFBI matrices are generated from recurrent solutions of the Eigenproblem, the application of complex topography of the 3-D surfaces and the subsequent processing provides non-linear results, such as PWL . Once the Onset Damage Criteria Eqs. (5,6) are fulfilled, proceed. Assume p-crack locations along the beam span to calculate matrices [ (2) 1 ( ? @ & , ) ] for 0< a c /D<0.5, m_mx using any of Eqs. (7-12), plot such 3-D created p matrices datasets, for instance, Fig. 2 which show two matrices, 3-D surfaces, for a) L c /L = 0.03, b) L c /L =0.23 assumed crack locations. An automated Matlab program executes tasks in a few minutes. Then, such a set generates [ BSFI ] matrices (for the p Lc assumed locations) that are subtracted from tested { SDI } k t damage index vectors experimentally are obtained, where super-index k denotes which BSFI k expression is used. Graphs and plots aid the method's explanation.

Figure 2. Distinctive nonlinear topography of the matrices [ (#) % ( & ( ' , ) ] computed for crack depth range, 0< a c /D <0.5, and maximum modes m_mx equal to 16. The two 3-D mesh surfaces are obtained for different assumed crack locations: a) L c /L = 0.03, and b) L c /L =0.23 . Then, [S, SS, SSS] matrices are derived as functions of both probable crack depth and location. Previous matrices are obtained by searching for the minor discrepancy between tests on the monitored beam and calculated [ SFBI ] and performing interpolations to get relevant data for each { DI } k t =0 vector, i.e., the zero-plane surface. Based on the minimum { DI } _n , the vectors that integrate [S], [SSS] are obtained, i.e., the ac value of each mode at the assumed Lc is predicted when { DI } k n_mn = 0, i.e., such numeric minimum discrepancy vectors { DI } k n_mn intersect the 0-plane surface. Lastly, based on statistics, both L c /L and a c /D are estimated for the Standard Error of the Mean (SEM), σ B = s x / √ , minimum value, used in Fig. 3b. Damage-characterizing parameter errors are obtained for 95% confidence intervals in each analyzed validating case. Tables and graphs show successful validation results. 5. Experimental Validation Successful Results Due to article space limitations, the four successfully realized experimental validation cases are briefly presented in two graphs in Figs. 3; this is although the experimented beam varied in materials and slenderness, and a poor equipment frequency band (an old triaxial accelerometer, progressively noisy and lower precision after 6.5 KHz) was used, which only allowed to consider a limited number of flexural modes, cases II and IV use 13 modes, case III has 14, and case I considers 16 (see the lengths of the lines in the horizontal axis in Figs. 3a,b). A future publication will contain a Flow Diagram of the method, details of the performed experiments, the beam materials, geometry, damage locations, and severity, i.e., the validation cases data, experimental set-up information, test equipment specifications, and their shortcomings, computed matrices and test vectors in the progressive application of the method, the diagnose results, their accuracy, explanatory analysis, and some experimental recommendations. Fig. 3a at LHS compares both the obtained SDI _t test vector on the analyzed beam to the