Application of the Finite Element Method to Rotary‐Wing Aeroelasticity

Abstract

Recent research in rotary‐wing aeroelasticity has indicated that many fundamental problems in this area are inherently nonlinear. The nonlinearities are due to the inclusion of finite slopes, due to moderate deflections, in the structural, inertia and aerodynamic operators associated with this aeroelastic problem. In this paper the equations of motion, which are both time and space dependent, for the aeroelastic problem are first formulated in P.D.E. form. Next, the equations are linearized about a suitable equilibrium position. The spatial dependence in these equations is discretized using a local Galerkin method of weighted residuals resulting in a finite element formulation of the aeroelastic problem. As an illustration, the method is applied to the coupled flap‐lag problem of a helicopter rotor blade in hover. Comparison of results with previously published solutions establishes the convergence properties of the method. It is concluded that this formulation is a practical tool for solving rotary‐wing aeroelastic stability or response problems.