A framework for integrating phononic materials in aerodynamic flows*

There is growing interest in integrating phononic metamaterials—materials with unique frequency-dependent properties arising from their periodic structure—into passive, adaptive flow control paradigms. To fully harness these structures in the intended control aim, clear methodologies must be developed to meaningfully quantify the fluid-structure interplay, including (i) identifying what canonical phononic material models can be utilized that enable interaction between key phononic material behaviors and flow processes such as vortex shedding, (ii) synthesizing dimensionless FSI parameters that allow for systematic tuning of phononic material behaviors relative to flow processes. In the spirit of addressing these questions, we consider an aerodynamic system equipped with a compliant surface whose motion is governed by a phononic material diatomic chain. We explore "ungrounded" and "grounded" configurations and discuss their relevance for point (i). We also introduce dimensionless parameters that relate key phononic material behaviors such as truncation resonance frequency, decay rate, and static structural stiffness to key flow behaviors such as vortex shedding timescales and mean lift on the compliant portion of the airfoil. This proposed approach enables a systematic assessment of the fluid-structure interaction for this phononic material-equipped system, and is a building block for enhancing aerodynamic performance through the strategic use of phononic materials.