Fluid Structure Interaction of Linear Viscoelastic Splitter Plate at Low Reynolds Number

The flow-induced deformation of a viscoelastic thin plate, attached to the rear of a circular cylinder subjected to laminar flow is numerically investigated. An in-house fluid-structure interaction code couples the sharp-interface immersed boundary method for fluid dynamics with a finite-element method for structural dynamics. Standard linear solid (SLS) model is used to represent viscoelasticity of plate which is governed by two parameters. First is the  ratio of non equilibrium to equilibrium Young modulus (R) and second is the ratio of structural viscosity to non equilibrium Young modulus (ζ). The present study is to examine the dynamic response of the viscoelastic plate by varying the parameter R and ζ for Reynolds number, Re =100.  The tip displacement amplitude (A_{Y_tip})  and time to achieve dynamic  steady state  has been investigated. Tip displacement amplitude is  non monotonic function of ζ. When forcing frequency is lesser (greater) than natural frequency of the plate, A_{Y_tip} decreases (increases asymptotically) .   The theoretical analysis of simple spring, mass, dashpot model of SLS is done to understand effect of sinusoidal force on the plate dynamics. Numerically  computed A_{Y_tip}  is observed to be similar trend as the  analytical result.