Flow-induced vibrations of a cantilevered flexible vertical plate.

We study the flow-induced vibrations of a flexible vertical plate cantilevered at its bottom at Re=100. We model our system by solving the 2D incompressible Navier-Stokes equations with the Continuity equation for the fluid and use the Saint-Venant Kirchhoff material model for the plate. The dynamic response of the plate is analysed at various reduced velocities obtained by varying its bending stiffness at a constant density ratio of 100 (equivalent to a mass ratio of 10). We plot the output frequency contours and variation in amplitude against reduced velocity to examine the plate lock-in characteristics with its first and second-mode natural frequencies. The plate is modelled as an Euler Bernoulli beam for calculating the approximate values of its modal frequencies. We find a plate response similar to vortex-induced vibrations (VIV), where the plate locks in and de-synchronizes with its natural frequencies as the reduced velocity changes. We identify four regions: (i) lock-in with the first mode, (ii) de-synchronization, (iii) lock-in with the second mode, and (iv) de-synchronization. The trajectories of a probe point (at the tip of the plate) are also plotted to qualitatively demonstrate the mean position and angular displacement variations with reduced velocity.