Uncertainty Characterisation of Locally Resonant Metamaterials for Design Optimisation

The past decade has witnessed a growing focus on vibro-acoustic metamaterials for vibration mitigation, owed to their ability to exhibit a frequency bandgap. This is a region where the vibration response is significantly reduced around a targeted resonance. The high degree of tunability of metamaterials for different applications and operating conditions makes them particularly appealing to design engineers. Recent research has pivoted around the optimisation of metamaterials unit cells to maximise the attenuation band and minimise the amplitude of the response in the frequency domain, hence showing better performance than traditional materials. Most modelling techniques for metamaterials rely exclusively on physics-based models and using the results to identify candidates for experimental testing. However, these models do not take into account uncertainties that arise in manufacturing, mounting, experimental data collection and inaccurate physics knowledge. Accounting for these uncertainties at the digital design step is essential towards obtaining metamaterials design that are robustly optimised under uncertainty. This work investigates the characterisation of various sources of uncertainties between different nominally identical Locally Resonant Metamaterials beams and plates. Through an experimental campaign, the built metamaterials are compared to their corresponding digital design in a Finite Element Model. Investigations on the influence of uncertainties of various sources are carried out, including part-to-part variability and different factors of manufacturing and assembly through Design of Experiments. Finally, the inclusion of uncertain inputs in a design optimisation framework and the related challenges are addressed, presenting some potential solutions.