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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characterization of 1-D circular beams. Starting with expressions for onset damage detection, the SFBI maps and method achieve locating it, characterizing, and evaluating its seriousness. Six innovating Bending Splitted-Frequency Indexes (BSFI j ), j=1, m_mx are presented for 1-D beams with open cracks, where m_mx is the highest number of bending modes considered, restricted by the test equipment quality. Damage detection and nonlinear characterization methods are applied to four experimental cases to validate the work. Only bending natural modes do split, as presented by Gomez-Mancilla et al. (2015) and at the IFToMM Congress (2014), so axial and torsional modes can be disregarded. The sudden release of enormous rotor kinetic energy has caused several catastrophes, Yamamoto, Ishida (2002). In Palacios-Pineda et al. (2017), damage detection and characterization in an operating rotor is realized. For the next-generation aircraft, an advanced SHM system was proposed by Lejeune et al. (2024). Dimarogonas et al. (1985, 2013) developed a hybrid application procedure involving Fracture Mechanics and circular rotors. Much effort has been devoted to creating low-cost, efficient techniques incentivizing technical and academic works. This work applies to the industry for NDT inspections, data-driven SHM, CM, and Very High Cycle Fatigue VHCF experiments aimed at defining international standard guidelines, Gomez-Mancilla (2024). The method relies on actual test data, acquisition & excitation software & hardware, and computing equipment. The work contains a brief theory in section 2, the innovative vibration-derived damage indexes, and their expressions in section 3; such a damage numeric model is implemented in Matlab code; in section 4, a developed nonlinear damage characterization method is presented. In section 5, a synopsis of four experimental cases and damage onset detection in a VHCF test rendered successful validation results. Discussion and Conclusions in section 6. 1.1. Modal Damage Indexes (DI), SFBI The innovative BSFI j modal damage indexes, restricted to flexural modes, are a principal tool. Modal vibration indexes have not been previously employed as DI . Given the abundance of criteria, assessing their efficacy is difficult when large civil structures are involved. Kappos (1997) studied indicators to classify damage indices, deterministic and probabilistically. In a structural health monitoring review 1996-2001, several damage approaches were given to detect damaged rotor vibrational behavior. Gomez-Mancilla (2004) analyzed the mass-imbalance vector interacting with a rotor crack; such an angle between both vectorial orientations is used as a model parameter. Maintenance only minimizes the omnipresent imbalance and re-appears when cracks nucleate. Previous 1-D beam works on bars and rotors restricted to analyzing crack modal data of a single-mode ξ-x vibration plane here named ω ξ_#m , where x goes along the beam span. Therefore, literature comparisons only involve ω ξ_#m . The stiffer orthogonal frequency ω η _#m has been ignored. Prominent SFBI peaks identify dangerous modes-frequencies, capture damage symptoms, and can be used as an SHM inverse identification while in operation. Efficient Modal Damage Indices (MDI) per each natural bending mode characterize crack problems in 1-D structures and can be applied to SHM, CM, and NDT techniques. This work presents six BSFI based on the split phenomenon, yet more MDI can be derived using flex frequency parameters, !" , # " , $ " , ! " = !# " − !$ " ;

Fig. 1 a) Circular finite element beam, shaded cracked section, 6 dof ; b) split natural frequency

integral-pristine ( 0 ), stiffer ղj -mode, softer ξ j -mode and their difference values, respectively, appear in all bending