Flutter of Partially Rigid Cantilevered Two-DimensionalPlates in Axial Flow

Abstract

The introduction of adaptive materials for active camber line shape control favors flexible wing designs, thus making adaptive wings more susceptible to instability phenomena. Motivated by a new wing concept for micro aerial vehicle applications, the aeroelastic stability of partially rigid cantilevered plates in an axial flow is investigated. The plate is modeled as a beam having a rigid and a flexible part. The beam is modeled using the classical Euler-Bernoulli bending theory, the unsteady aerodynamic pressure is modeled using Theodorsen's theory, and the Rayleigh-Ritz method is used to obtain a discrete model. Stability analysis is carried out in Laplace's domain. The results indicate that a partially rigid cantilevered plate in an axial flow does not show static aeroelastic divergence but exhibits dynamic aeroelastic instability. The flutter velocity at which this instability occurs is dependent on the ratio of the flexible length to the total length of the plate and the mass ratio. Adding a rigid part ahead of a flexible plate can have a stabilizing or destabilizing effect on the aeroelastic behavior of the flexible plate, depending on the mass ratio. The phase-angle difference between the upstream and downstream part of the two-dimensional plate is shown to be dependent on the mass ratio and flexible length fraction. Jumps in the flutter diagram occur because of changes in flutter mode, and the flexible length fraction also affects these jump phenomena. The jumps are shown to be the result of eigenvalue branch collision. There are multiple critical flow conditions for mass ratios around the jumps. Therefore, a new practical flutter boundary definition is introduced to remove the overlap between flutter modes near the jumps. The flutter diagram calculated according to the new definition shows better agreement with published time domain simulations.