A framework to systematically study the nonlinear fluid-structure interaction of phononic materials with aerodynamic flows

Phononic materials (PMs) are periodic media that exhibit novel elastodynamic responses. While PMs have made progress in vibration-mitigation applications, recent studies have demonstrated the potential of PMs to passively and adaptively modulate flow behavior through fluid-structure interaction (FSI). For example, PMs have been shown to delay laminar-to-turbulent transition and mitigate unsteadiness in shock-boundary layer interactions. However, a systematic framework to relate the effect of specific PM behaviors to the FSI dynamics is lacking. Such a framework is essential to systematically investigate the complex and nonlinear coupled dynamics of the FSI. Further, parameters that are not typically considered in PM models become critical, such as the vibration amplitude. This article addresses this gap by proposing FSI-relevant ``behavioral'' parameters, distinct from the structural parameters of the PM, but with a clear mapping provided to them. We use high-fidelity, strongly coupled simulations to quantify the FSI between a novel configuration of laminar flow past a flat plate, equipped with a PM. Our study proposes four critical PM behavioral parameters -- effective stiffness, truncation resonance frequency, a quantity representing the dynamic displacement amplitude, and unit cell mass -- that influence the spectral characteristics of the vortex-shedding process inherent to the flat plate system. Results show connections between each parameter and distinct behavior in the lift coefficient in FSI. While the focus of this work is on the PM-FSI dynamics in an aerodynamic flow, we argue that identifying these behavioral parameters is key to unlocking scientific study and design with phononic materials in fluid flows more broadly.