Nonlinear Normal Modes For Damage Detection: Analytical Results and Experiments

The use of nonlinearities in damage detection is a potential avenue for developing accurate monitoring systems in a variety of engineering applications. In several situations the linear theory reveals its drawbacks, for example, when environmental disturbances affect the structural response. For instance, the thermal effects can induce frequency shifts of the same order of magnitude of the damage itself [1] and, for properly accounting them, accurate nonlinear models become necessary [2]. In this prospective, it is interesting to ascertain if the nonlinear response is more sensitive to damage than the linear one. The nonlinear normal modes concept (NNMs) lends itself naturally to extend the consolidated knowledge of the linear theory [3]. The sensitivity of the nonlinear dynamic response to damage is investigated considering a straight beam clamped at both ends with localized reductions of the cross-sectional area in different positions along the beam span. In the first stage, the problem is analytically tackled with the method of multiple scales for computing the NNMs and the backbones curves. The trends of the effective nonlinearity coefficient for the lowest bending mode as function of the damage position and severity are obtained and compared with those of the linear frequencies. In the second stage, an experimental campaign is carried out on a set of steel beams with different levels of area reduction within a few segments along the beam span. The analytical results are qualitatively corroborated by tailored experiments confirming the important role that the nonlinear structural response can play towards damage detection.