Investigating and exploiting the impact of variability in resonator parameters on the vibration attenuation in locally resonant metamaterials

Locally resonant metamaterials (LRMs) have recently emerged in the search for lightweight noise and vibration solutions. These materials have the ability to create stop bands, which arise from the sub-wavelength addition of identical resonators to a host structure and result in strong vibration attenuation. However, their manufacturing inevitably introduces variability such that the system as-manufactured often deviates significantly from the original as-designed. This can reduce attenuation performance, but may also broaden the attenuation band. This work focuses on the impact of variability within tolerance ranges in resonator properties on the vibration attenuation in metamaterial beams. Following a qualitative pre-study, two non-intrusive uncertainty propagation approaches are applied to find the upper and lower bounds of three performance metrics, by evaluating deterministic metamaterial models with uncertain parameters defined as interval variables. A global search approach is used and compared with a machine learning (ML)-based uncertainty propagation approach which significantly reduces the required number of simulations. Variability in resonator stiffnesses and masses is found to have the highest impact. Variability in the resonator positions only has a comparable impact for less deep sub-wavelength designs. The broadening potential of varying resonator properties is exploited in broadband optimization and the robustness of the optimized metamaterial is assessed.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.