Numerical, statistical and experimental investigation on damage quantification in beams from modal curvature

Synthesis of healthy-structure model responses for damage quantification

“…This relation is derived in section 2.3 of ref. 19. In that work, it was numerically and statistically shown that the apparent damage extent 2 h d of a single crack is strongly related to the beam cross-section height h s , and it is almost independent on the crack depth, that is, h d ≈ h s /2.…”

“…This important fact and the application of a procedure similar to the one described in ref. 19 lead to a more accurate interpretation of equation (2) when the quotient of numerical derivatives are used: The calculated indicator is the reduction in the mean stiffness, which unfortunately depends on the sensor separation h , and therefore, it is not a direct quantifier of damage. That is…”

“…Here, 2 h d is the damage apparent extent, which is related to Saint Venant’s principle, as discussed in ref. 19; and 2 h * is the length of the interval in which the derivative is implicitly averaged by the numerical differentiation formula.…”

“…Equation (27) also relies on the assumption that d i ( x ) does not change sign in the interval [ x d − h *, x d + h *] for applying the Weighted Mean Value Theorem (Appendix D in ref. 19).…”

“…Such a possibility was recently introduced in ref. 19 for simply supported beams. There, it was assumed that the bending moment remains approximately constant after damage (hence the simple support condition).…”