Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

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 areodynamic 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 linearized 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 condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation 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. 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.

[1]  Peretz P. Friedmann,et al.  Some conclusions regarding the aeroelastic stability of hingeless helicopter blades in hover and in forward flight , 1973 .

[2]  J. E. Burkam,et al.  Exploration of Aeroelastic Stability Boundaries with a Soft-in-Plane Hingeless-Rotor Model , 1972 .

[3]  John C. Houbolt,et al.  Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades , 1957 .

[4]  Peretz Friedmann,et al.  Influence of structural damping, preconing offsets and large deflection on the flap-lag-torsional stability of a cantilevered rotor blade , 1975 .

[5]  Dewey H. Hodges,et al.  Nonlinear Equations for Bending of Rotating Beams with Application to Linear Flap-Lag Stability of Hingeless Rotors , 1973 .

[6]  J Mayo Greenberg,et al.  Airfoil in sinusoidal motion in a pulsating stream , 1947 .

[7]  Maurice I. Young,et al.  A Theory of Rotor Blade Motion Stability in Powered Flight , 1964 .

[8]  P. Tong,et al.  Non-linear flap-lag dynamics of hingeless helicopter blades in hover and in forward flight , 1973 .

[9]  R. E. Hansford,et al.  Torsion-Flap-Lag Coupling on Helicopter Rotor Blades , 1973 .

[10]  David A. Peters,et al.  An approximate solution for the free vibrations of rotating uniform cantilever beams , 1973 .

[11]  Kurt H. Hohenemser,et al.  Aeroelastic Instability of Torsionally Rigid Helicopter Blades , 1967 .

[12]  Peretz P. Friedmann,et al.  Aeroelastic Instabilities of Hingeless Helicopter Blades , 1973 .

[13]  Dewey H. Hodges,et al.  Stability of elastic bending and torsion of uniform cantilevered rotor blades in hover , 1973 .

[14]  P. Friedmann,et al.  Investigation of some parameters affecting the stability of a hingeless helicopter blade in hover , 1972 .

[15]  H. Huber,et al.  Effect of Torsion-Flap-Lag Coupling on Hingeless Rotor Stability , 1973 .

[16]  Earl H. Dowell,et al.  Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades , 1974 .

[17]  Dewey H. Hodges,et al.  Linear Flap-Lag Dynamics of Hingeless Helicopter Rotor Blades in Hover , 1972 .

[18]  David A. Peters,et al.  Technical Notes: The Effects of Second Order Blade Bending on the Angle of Attack of Hingeless Rotor Blades , 1973 .