A numerical study on flapping dynamics of a flexible two-layered plate in a uniform flow

Abstract

Over the past few decades, energy generation from piezoelectric patches mounted on a flexible flat plate exhibiting flapping motion has gained attention. Piezoelectric patches are generally multilayered consisting of piezoelectric, substrate, and electrode layers placed on top of each other. Although the flapping dynamics of single-layered structures have been extensively studied, understanding the flapping dynamics of multilayered structures is minimal. We propose a quasi-monolithic formulation with exact interface tracking to simulate the fluid-multilayered structure interactions. The proposed formulation is validated by considering a simple two-layered plate-like structure with identical material properties against a single-layered plate. We then use this formulation to perform parametric simulations by providing different material properties to each layer of the plate to understand the effect of differences in the material properties on the flapping dynamics. The simulations are performed by selecting different values of Young's modulus and density for each of the layers such that the average structure-to-fluid mass ratio m*avg=0.1 and the average non-dimensional bending stiffness KBavg=0.0005 remain constant for a Reynolds number Re = 1000. First, the effects of difference in elasticity between the two layers on the flapping amplitude, frequency, forces, and vortex shedding patterns are investigated. Following this, the effect of differences in elastic properties on the onset of flapping is investigated for a case with Re = 1000, m*avg=0.1, and KBavg=0.0008, for which a single-layered plate does not undergo self-sustained flapping. Two distinct response regimes are observed depending on the difference in elastic properties between the two layers: (I) fixed-point stable and (II) periodic limit cycle oscillations. Finally, we look into the effects of structural density differences on the flapping dynamics of a two-layered plate.