Flutter instability of a thin flexible plate in a channel

Abstract

The stability of a thin flexible plate confined inside an inviscid two-dimensional channel is examined using a nonlinear eigenvalue analysis method. A new Green’s function for the vortex wake of the flexible plate inside the channel, as well as its rapidly convergent series approximation, is proposed. Comparison with a fully coupled Navier–Stokes fluid–structure interaction model indicates that the current inviscid model successfully predicts the flutter boundary for a confined flexible plate. The analysis also shows that confinement has a destabilizing effect on heavy plates. Furthermore, as the confinement is increased, the oscillating frequency of the plate increases and new peaks appear in its stability curve. Asymmetric placement of the plate within the channel, especially when the plate is very close to one wall, also modifies the stability curve of the system by shifting the mode transition points toward smaller fluid-to-plate inertia ratios. Our study suggests that the degree of confinement and asymmetric placement of the plate in the channel could be used to alter the flutter instability of the plate, and to adjust the frequency of flutter.