Nonlinear Normal Modes For Damage Detection: Theoretical Concepts And Preliminary Experimental Validation

The exploitation of nonlinearities in the eld of damage detection is a promising direction towards robust and reliable monitoring systems for engineering applications. In this perspective, the concept of nonlinear normal mode (NNM) is a natural candidate for extending the knowledge already established in the linear framework and for developing new approaches. A clamped-clamped beam with localized cross-sectional reductions across the beam span is considered. The problem is first analytically tackled via the method of multiple scales for computing the NNMs and the backbone curves. The latter describes the dependence of the resonance frequencies on the oscillation amplitude and are governed by the so-called effective nonlinearity coefficient for each mode. Subsequently, an experimental campaign is carried out considering an undamaged and a damaged beam to validate the analytical results. The effective nonlinearity coeffcient is shown to exhibit a sensitivity to damage higher than that exhibited by the linear natural frequencies, whereas the backbones associated to each mode reveal an interesting dependence on the sti ness reduction and damage location.