The ability to favorably control unsteady aerodynamic phenomena is key to the design of the next generation of unmanned aerial vehicles (UAV). Comprehensive control of these flows remains elusive due to the high dimensional, nonlinear, and frequency-dependent nature of most aerodynamic flows. State of the art flow control efforts have been utilized successfully in a variety of scenarios, but there remain challenges in developing fast, cheap actuation mechanisms as well as in utilizing models for the complex flow dynamics that can be used to make real-time decisions about how to update actuation using some (limited) flow information. In this work, we explore an alternative approach, where phononic materials are exploited for passive, adaptive unsteady aerodynamic flow control. Phononic materials are materials that possess intrinsic frequency-dependent characteristics due to their periodic structure. This property is particularly promising for aerodynamic flows, which have inherent frequency-rich dynamics. In this vein, we use high-fidelity simulations to investigate the fluid structure interaction (FSI) dynamics that ensue between a phononic material and an aerodynamic flow and identify the effect of key driving FSI parameters on the aerodynamic performance (e.g., lift). We consider a Reynolds number of 500—relevant to micro-and smaller-scale unmanned aerial vehicles—and model the phononic material as a bi-layer Euler-Bernoulli beam. We introduce meaningfully chosen non-dimensional parameters that drive the FSI dynamics of the system. These parameters allow for partitioning of effects due to (i) effective uniform material properties and (ii) properties due to the non-uniform nature of the phononic material. This representation enables a systematic assessment of how the various phononic material regimes impact aerodynamic performance. We also give results that demonstrate some effects of the dimensionless parameters on the FSI system dynamics.