Aero-servo-viscoelastic flutter and torsional divergence alleviation for a wing in subsonic, compressible flow

The theory of aero-servo-viscoelasticity first developed by the authors¹ is extended to the subsonic, compressible flow regime for a rectangular wing. The subsonic flow is modeled using the Possio integral equation and the closed form solution derived by Balakrishnan.² Of interest is the effect of varying viscoelastic properties and servo controller gains on the flutter boundary and torsional divergence speeds of the wing. The viscoelastic properties are the relaxation times and the ratio of initial to final moduli. The three controllers considered are the proportional, integral, and differential feedback controllers. The solution procedure for calculating the flutter boundary and torsional divergence speeds uses the extended Theodorsen function derived by Sears³ that includes both reduced damping and reduced frequency. This formulation can model both torsional divergence and flutter. Within MATLAB™, the governing equations for the wing are solved numerically using an iterative procedure. The results of extending aero-servo-viscoelasticity to the subsonic, compressible flow regime are pertinent for the design of UAVs and MAVs with fixed or movable lifting surfaces for constant flight velocities. Further research is pursued for variable flight velocities that exist during maneuvers because viscoelastic materials have a memory effect. The variable flight velocities also require extensions to the unsteady aerodynamic formulations.