Abstract Summary
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 and result in strong vibration attenuation. 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. In this work, variability is exploited in view of broadening the vibration attenuation band of metamaterial beams. To this end, the design parameters of the metamaterial beam’s resonators are optimized in an allowed design space around their nominal, identical values to obtain a wider frequency range of vibration attenuation. To account for uncertainties early in the design phase, when often little information concerning the inherent variability is available, the resonator design parameters are defined as interval uncertain variables and vibration attenuation performance bounds are computed. By formulating a fitness function which allows trading-off vibration attenuation performance and performance robustness in terms of these performance bounds, optimal resonator design parameters are sought which enable robust vibration attenuation band broadening. To solve the above optimization problem, a global search approach can be followed. However, as the required amount of model evaluations for optimizing the performance and finding the performance bounds rapidly grow, using a global search approach can become prohibitively expensive especially for large models. Instead, this work explores the use of a recently proposed machine learning based non-intrusive uncertainty propagation approach to efficiently evaluate upper and lower performance bounds with a limited amount of model evaluations. Moreover, as the approach is based on a Gaussian Process regression model and Acquisition Functions, additional metrics can be introduced to assess if the obtained bounds are satisfactory. The robust optimization approach is applied to a simplified metamaterial beam with periodic mass-spring-damper resonators to investigate the importance of accounting for the robustness against design parameter variations in metamaterial performance broadening.
