Interval uncertainty propagation in metamaterial beams using machine learning based optimization

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Metamaterials have recently emerged in the search for lightweight noise and vibration solutions. One of their appealing properties for noise control engineering is the ability to create stop bands, which are frequency ranges without free wave propagation. These stop bands arise from the sub-wavelength addition of identically tuned resonators in or on a host structure. However, when manufacturing metamaterials, variability in material properties and geometry is inevitably introduced. On the one hand, the metamaterial attenuation performance can deteriorate due to variability, while on the other hand, variability can even broaden their typically narrowband performance. During the early phases in the design, when often little information concerning the inherent variability is available, it would be desirable to be able to assess the input uncertainty effects on the performance of metamaterials. This work focuses on the numerical assessment of the impact of uncertainties in resonator properties on the vibration attenuation performance of metamaterial beams. To this end, a machine learning based optimization strategy, the so-called Bayesian optimization, is employed in a recently developed non-intrusive uncertainty propagation approach. This enables a very efficient evaluation of the upper and lower bounds on the metamaterial performance, with the uncertain resonator parameters defined as interval variables.