A frequency-domain flutter solver for rotary-wing aeroelasticity

Abstract

A frequency-domain flutter solver for rotary-wing aeroelasticity is presented. The method applies to linear time-periodic (LTP) aeroelastic systems, including helicopters in forward flight, propellers with yaw angle, and wind energy turbines. It assumes a frequency-domain representation of the aerodynamic model, using the aerodynamic harmonic transfer function (HTF), denoted here as the harmonic generalized aerodynamic force (GAF) matrix. This accounts for the effects of harmonics of the fundamental or forcing frequency. The harmonic GAF exhibits a nonlinear dependence on the Laplace variable, and after coupling with the structural model, the relevant subset of Floquet exponents is determined by solving a nonlinear eigenvalue problem. This method extends the conventional flutter solvers used in fixed-wing aeroelasticity, which are based on a linear time-invariant (LTI) system. Specifically, it introduces harmonic extensions of the p-k and g flutter solvers, termed the h-p-k and h-g solvers, making them applicable to rotary-wing aeroelasticity. When applied to an LTI system, the method naturally reduces to the standard p-k and g flutter solvers used in fixed-wing aeroelasticity. The proposed method is demonstrated on a two-degree-of-freedom rotor blade section in forward flight, incorporating an unsteady aerodynamic model based on potential flow theory. It accurately predicts the same advance ratio for flutter onset as the Floquet method while eliminating the need to construct the monodromy matrix. Furthermore, it enables stability analysis even when the aerodynamic model is not available in state-space form, allowing for the use of nonparametric aerodynamic representations.