Coupling of a State-Space Inflow to Nonlinear Blade Equations and Extraction of Generalized Aerodynamic Force Mode Shapes

The aeroelastic stability of helicopter rotors in hovering flight has been investigated by a set of generalized dynamic wake equations and hybrid equations of motion for an elastic blade cantilevered in bending and having a torsional root spring to model pitch-link flexibility. The generalized dynamic wake model employed is based on an induced flow distribution expanded in a set of harmonic and radial shape functions, including undetermined time dependent coefficients as aerodynamic states. The flow is described by a system of first-order, ordinary differential equations in time, for which the pressure distribution at the rotor disk is expressed as a summation of the discrete loadings on each blade, accounting simultaneously for a finite number of blades and overall rotor effects. The present methodology leads to a standard eigenanalysis for the associated dynamics, for which the partitioned coefficient matrices depend on the numerical solution of the blade equilibrium and inflow steady-state equations. Numerical results for a two-bladed, stiff-inplane hingeless rotor with torsionally soft blades show the importance of unsteady, three-dimensional aerodynamics in predicting associated generalized aerodynamic force mode shapes.