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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numerically simulated equivalent SDI_ n vector, where computations for flexural modes for each case use parameters from the four method diagnosed crack locations and depths, L c /L, a c /D , resp. RHS of Fig. 3b also illustrates the method's final validation results; the progressively improved numeric matrices are calculated for each assumed crack location till arriving at [S], [SS], [SSS] , which encompass crack location L c /L and crack depth a c /D , for each mode. The error ( SEM ) minimum value provides the best-diagnosed crack location, i.e., the four diagnosed L c /L are: 0.13, 0.30, 0.34, 0.49. Gomez-Mancilla (2024) used this work successfully to detect the damage onset in a VHCF test monitoring bending, where the frequency splits occurred for the first and second harmonic bending responses, i.e., BSFI j ≠ 0, j=1,2. 6. Discussion and Conclusions The method is a nonlinear 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 processing provides nonlinear results, such as PWL . For the first time, damage indexes obtained from the vibration response of the monitored structure are developed and used in a nonlinear characterization and damage assessment method. To enhance the effectiveness of the SFBI indexes and method, the principal limitation is simple and easy to overcome: Just use broadband frequency testing equipment. As in most real-life engineering applied cases, the nonlinear diagnosis and structural damage characterization method relies on test data, transformation to SFBI _t , some matrixial computations, and basic statistics such as minimum discrepancy error. That is, the technical specifications of the testing equipment should be broadband capable of acquiring a good number of flexural natural frequencies of the monitored beam, say thirty or more. Details showing the excellent work achievements and validating by experiments in laboratory tests and detecting damage at the onset of it in VHCF experiments will be presented in a future publication Gomez-Mancilla (2024).

Fig. 3. Validation results of the four experimental cases. a) discrepancy vectors, both test-computed & numerically obtained vs. bending modes, both yield excellent similar results; b) SEM error vs. the assumed crack locations; the best diagnoses are those having the minimum error values.

Acknowledgments The author is grateful for the scholarship support the Sistema Nacional de Investigadores S.N.I.I provided . CONACHyT , México, and my colleague Prof. Juan Alfonso Beltrán Fernández. References Darpe A.K., K. Gupta K., Chawla A., 2004. Coupled Bending, Longitudinal And Torsional Vibrations of a Cracked Rotor, J. Sound Vib., 2004, doi: 10.1016/S0022-460X(03)00003-8. Dimarogonas A.D., Paipetis S.A., Chondros T.G.,1985, 2013. Analytical Methods in Rotor Dynamics, (1st, 2nd Eds.) 1985, 2013.