Non-dimensional parameters for the flapping dynamics of multilayered plates

The coupled flow-induced flapping dynamics of flexible plates in uniform axial flows are governed by three non-dimensional numbers, namely: Reynolds number $(Re)$, mass-ratio $(m^*)$, and non-dimensional flexural rigidity $(K_B)$. The traditional definition of these parameters is limited to isotropic single-layered flexible plates. However, there is a need to define these parameters for a more generic plate of multiple isotropic layers placed on top of each other. In this work, we derive the non-dimensional parameters for a flexible plate of $n$-isotropic layers and validate the non-dimensional parameters with numerical simulations. The proposed non-dimensional framework connects the experimental, numerical, and analytical studies on single-layered plates with the flapping dynamics of multilayered plates.