Resonant metamaterial designs for a broadband mitigation of flow-induced vibrations

Resonant metamaterials have recently emerged as lightweight and performant noise and vibration solutions for the hard-to-address low-frequency ranges. These engineered materials are made by an assembly of resonant elements onto a host structure. Their interaction leads to tuneable frequency ranges, known as stop bands, in which they can outperform classical noise control measures. However, these stop bands have a limited frequency range effect. To broaden the noise and vibration performance also outside the stop band, this paper presents a design approach for a finite resonant metamaterial plate. Two regularly spaced grids of resonant elements are both added to a plate. In the first grid, the resonant elements are tuned to the same nominal frequency and stop band behaviour is achieved. In the second grid, the tuned frequency of each resonant element is found through an optimisation procedure, with the goal of minimising the dynamic response of the plate outside the stop band. To speed up the optimisation, model order reduction and a dynamic sub-structuring method are employed. The performance of this finite resonant metamaterial plate design is validated by evaluating its vibration response due to a broadband grazing flow excitation and comparing it to a plate with equivalent mass additions.