The use of modal curvatures for damage localization in beam-type structures

• We derive an analytical expression of the modal curvature difference of damaged beams.
• The modal curvature difference could have several peaks outside the damage region.
• The amplitude of these peaks is quantified against damage position and width.
• A suitable filtering procedure to reconstruct the damage shape is presented.
• The procedure is effective for multiple damages either concentrated or distributed.

The localization of stiffness variation in damaged beams through modal curvatures, i.e., second derivative of mode shapes, is studied by exploiting a perturbative solution of the Euler–Bernoulli equation. It is shown that for low order modes the difference between undamaged and damaged modal curvatures has only one distinct peak if the damage is localized in a narrow region. This phenomenon is independent of the presence of experimental noise and of the technique used to reconstruct the curvature mode shapes from the displacement mode shapes. Broader damages cause the modal curvature difference to have several peaks outside the damage region that could result in a false damage localization. The same effect is present at higher modes for both narrow and broad damages. As a result, modal curvatures can be effectively used to localize structural damages only once they have been properly filtered. Here the perturbative solution is used to introduce an effective damage measure able to localize correctly narrow and broad damages and also single and multiple damages cases.