Fluid-structure interaction of a phononic bi-layer flat plate with an aerodynamic flow*

Passive, adaptive flow control strategies offer significant promise in overcoming the challenges associated with active flow control. We explore the fluid structure interaction (FSI) of flexible phononic materials towards this aim. Phononic materials are architected materials with frequency-dependent characteristics that arise from their periodic structure. In this study, we investigate the FSI between an aerodynamic flow and a phononic material defined by a bi-layer flat plate. The flat plate is modeled as a clamped-clamped linear Euler-Bernoulli beam with a periodic mass and stiffness distribution throughout the entire length of the beam. We perform high-fidelity 2D numerical FSI simulations of unsteady flow past the bi-layer flat plate at Re=500 and an angle of attack of 15 degrees. The nonlinear simulations are initiated from a formal base state of the FSI system. The analysis will focus on the ensuing limit cycle interplay between the plate vibrations and the vortex-shedding process. The effect of various phononic material parameters (equivalent mass, equivalent stiffness, periodicity) on the nature of the limit cycle will be characterized. A global stability analysis will then be employed to mechanistically explain the system's departure from the base state, with a detailed analysis of the nonlinear simulation data used to investigate the long-time nonlinearly saturated dynamics. In this process, we will also identify the relevant structural parameters that lead to performance benefits/detriments (lift,drag) of the phononic flat plate as compared to the baseline rigid flat plate flow configuration.