Vibration attenuation performance prediction in metamaterials: An efficient computational approach addressing parametric uncertainties

Mechanical metamaterials have proven useful for vibration attenuation applications. Nevertheless, uncertainties during the manufacturing process affect their expected performance as each substructure deviates from the nominal characteristics. To account for this, uncertainty quantification at the structural level must be performed, potentially involving a significant computational cost. In this study, a novel computational framework is developed to accelerate the vibration attenuation performance identification in metamaterials under uncertainties associated with model parameters. The uncertainty quantification is based on Monte Carlo Simulations (MCS) at the structure level, allowing each unit cell to have independent model parameters and avoiding the assumption of infinite periodic lattices. The computational overload of the recursive computation of high-fidelity simulations demanded by the MCS is avoided by the novel integration of a Craig–Bampton (CB) mode synthesis, stiffness matrix perturbations, and a Kriging surrogate model. The CB method partitions the metamaterial into small substructures simultaneously to perform a modal reduction of the mass and stiffness matrices at the substructural level. The perturbation strategy is imposed over a baseline model and is applied to each substructural CB-reduced stiffness matrix. The Kriging model provides an approximation to predict the perturbation magnitude for a new set of model parameters. Three example problems are developed to illustrate the accuracy and implementation of the method. These results showcase how the uncertain vibration attenuation performance predictions of the metamaterial can be achieved at a reduced computational cost, allowing for uncertainty quantification analysis of metamaterials at tractable speeds.