Stability of elastic bending and torsion of uniform cantilevered rotor blades in hover (original) (raw)

14th Structures, Structural Dynamics, and Materials Conference

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and aero dynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a 1inear:zed stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating con dition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approxi mation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. A structural coupling parameter 6? is introduced to simulate variations in flap-lag structural coupling that arise for blades having nonuniform stiffness distributions. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics. The stability of torsionally flexible blades is strongly influenced by the effects of the bending-torsion sturctural coupling. Without precone, typical configurations are usually stable except for low values of 6? or low torsion frequencies. Addition of precone is strongly destabilizing for a wide range of configurations. Except for very low torsion frequencies, the results also indicate that the structural terms in the torsion equation dominate the torsion inertia and damping terms which permits the use of an approximate, but simplified, system of equations with fewer degrees of freedom. Finally, the accu racy of the results is sensitive to the number and type o f mode shapes used in the analysis.