Resonant metamaterials have attracted significant research interest in mechanical and acoustic engineering with applications in the fields of sound and vibration control thanks to their integrated tuned mass dampers. One prevailing issue regarding industrial application of such structures is the high probability of local damage for their resonating parts. Accurate and efficient health state estimation methods for resonant metamaterials are therefore urgently required. In particular, the quantification and localization of damaged resonators represent key pieces of information for the operator of a structural asset. This work presents for the first time an investigation into quantifying and identifying damaged oscillators in a resonant metamaterial based on the measured frequency response function (FRF) data. Both data-driven and physics-based methods are implemented and corresponding results are exhibited. Manufacturing-induced structural uncertainty is quantified through physical measurements and taken into account in this work. It is demonstrated that such uncertainty may have a rather significant impact on the response of 3D printed resonant metamaterials, leading to difficulties vis-a-vis damage quantification. The proposed theoretical developments are able to properly account for such uncertainties, providing probabilistic estimation indices for the existing damage level and location. Both simulated and experimental case studies are presented to validate the two proposed methodologies and comparisons are also exhibited and discussed.
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