Bending Splitting-Frequency Index (BSFI) a Nonlinear Method & Damage Characterization for 1-D Vibration-based SHM

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 Δω0j 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.