PSI - Issue 68

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2025) 000–000 Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 68 (2025) 318–324

European Conference on Fracture 2024 Bending Splitting-Frequency Index (BSFI) a Nonlinear Method & Damage Characterization for 1-D Vibration-based SHM Gomez-Mancilla Julio C. a * a Laboratorio de Vibraciones & Rotodinamica, UPALM, Lindavista, CDMX, 07738, Mexico Abstract Today, industrial safety requires SHM, NDT, and CM to minimize risks and maintain safety standards at a competitive cost. Here, monitored modal response is the method's backbone. Fracture mechanics and J-Integral concepts in a FEM program model an open crack beam where modal-damage indexes extract the problem symptoms. Six innovative Mode Damage Indexes (MDI) in circular 1-D cracked beams focus on the bending frequency split. Bending Splitting-Frequency Indexes (BSFI j ) are imprinted by damage: cracks, pseudo-cracks, PSB, and structural weakening; BSFI peaks indicate dangerous modes. The damage model is validated vs. literature limit to plane ξ-x; ɳ-x split frequencies are added. Solving Eigenproblems, a Piecewise Linear PWL approximation allows a nonlinear analysis. Using ω0j and {SDI_ t } > 0 criteria, notches, imperfections, and unsymmetric pristine beams allow onset damage detection. An inverse algorithm calculates BSFI_ n maps at p- assumed crack locations; a test- BSFI_ t vector minimizes discrepancies. A flow diagram explains the method, damage detection, characterization, location, and severity. Tables, plots, and statistical parameters for four cracked cases, and onset damage detection in VHCF validate this work. © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers. Keywords: SHM; NDT; BSFI; damage indexes; experiment; validation; PWL ; onset damage ID; crack; fracture mechanics; eigen analysis; FEM. 1. Introduction Nowadays, practically all machines, structures, and devices must comply with strict compulsory safety guides and regulations. To maintain high safety standards and minimize risks at a competitive cost, the industry must monitor SHM online. The work aims to develop innovative DI, BSFI, and a nonlinear method to be applied to structural damage © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers

*Corresponding author: Gomez-Mancilla Julio C., Tel.: +52-55-1531-3619. E-mail address: gomezmancilla@gmail.com

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of ECF24 organizers 10.1016/j.prostr.2025.06.060