Dynamic response of a cantilevered flexible vertical plate in a uniform inflow at Re = 100

Abstract

We numerically study the dynamic flow-induced vibration (FIV) response of a flexible vertical plate cantilevered at its bottom in a two-dimensional flow at Reynolds number, Re = 100. The incompressible Navier–Stokes and continuity equations are solved for fluid flow, and the Saint Venant–Kirchhoff material model is used for the structure. Plate dynamics is studied concerning reduced velocity, which represents the ratio of solid to fluid dynamic time scales. A parametric study is performed by sweeping through its bending stiffness (or the non-dimensional elasticity) at a constant mass ratio of 10. The dynamic characteristics are studied in terms of amplitude and frequency variation of plate oscillations against the reduced velocity. The oscillation frequencies of the plate are compared with its first and second-mode natural frequencies to understand the lock-in behavior. The modal frequencies are calculated by approximating the plate as an Euler–Bernoulli beam. The observed response is broadly categorized into four regimes: (i) lock-in with the first mode, (ii) de-synchronization, (iii) lock-in with the second mode, and (iv) de-synchronization. Overall, the plate locks in and de-synchronizes with its natural modes as the reduced velocity changes. This behavior is similar to Vortex-Induced Vibrations (VIV) of an elastically mounted rigid cylinder.