Response of a linear viscoelastic splitter plate attached to a cylinder in laminar flow

Abstract

The flow-induced deformation of a viscoelastic thin plate attached to the lee side of a circular cylinder subjected to laminar flow is numerically investigated. An in-house fluid–structure interaction solver couples the sharp-interface immersed boundary method for fluid dynamics with a finite-element method for structural dynamics. Extending published results on elastic materials, the Standard Linear Solid (SLS) model is used to represent viscoelasticity of the plate, governed by the following two parameters: (a) the ratio of the non-equilibrium to equilibrium Young’s modulus (R), and (b) the ratio of dimensionless material damping to the dimensionless non-equilibrium Young’s modulus (τ). The focus of the present study is to examine the dynamic response of the viscoelastic plate at Reynolds number of Re=100. The amplitude and the time to achieve a dynamic steady state of a plate with 0.1<R<5 and 0.1<τ<10 have been investigated. The plate attains a self-sustained time-periodic oscillation with a plateau amplitude for the range of R=[0.1–5] for all values of τ. The dimensionless tip displacement amplitude (AY,tip) is found to be a non-monotonic function of τ. When the forcing frequency (vortex shedding frequency) is lesser (greater) than the natural frequency (considering the equilibrium Young modulus) of the plate, AY,tip decreases (increases) asymptotically. The theoretical analysis of a simple spring–mass–dashpot model of SLS is undertaken to understand the effect of sinusoidal forcing on the plate dynamics. Analytical predictions show general agreement with the non-monotonic behaviour of the numerically computed AY,tip. The results suggest that careful tuning of the damping may be effectively employed to enhance power output for energy extraction applications or to suppress flow-induced vibration when it is detrimental to the structure.