Effect of a Nonlinear Energy Sink on the Post-flutter Behaviour of High Aspect Ratio Wings

In this paper, the efficacy of using a Nonlinear Energy Sink (NES) to achieve a reduction in the post-flutter response of high aspect ratio wings has been investigated. The wing has two degrees of freedom in bending and torsion and is modelled as a 3 rd order beam with cubic stiffness nonlinearities, accounting for the bending curvature and inertia effects of high aspect ratio wings. The unsteady incompressible aerodynamic loading is simulated using Wagner’s indicial lift model and a NES is attached to the wing spar via a linear viscous damper and a nonlinear spring with cubic stiffness. The coupled equations of motion are discretised using Galerkin’s method and converted into a state space model that is integrated numerically. Following this, the structural equations are validated against experimental results, whilst the aerodynamic model is verified against similar computational models. The effect of the NES mass, stiffness and placement in both chordwise and spanwise directions on the wing post-flutter is investigated. The efficiency of the device is improved for higher mass ratios, however, the stiffness coefficient is sensitive to the flow speed and therefore the capability for an active NES device to have tuneable stiffness is one that shows promise. The findings also demonstrate that the optimum placement for the NES in the spanwise coordinate is a function of the flow speed and the stiffness ratio of the wing model. From the initial findings a device is tuned with the target to reduce the limit cycle oscillation (LCO) amplitude in the immediate post-flutter region. The tuned NES achieved a 3.5% delay in the bifurcation and a reduction in the bending and torsion tip deflections of 84.9% and 89.5% respectively.