Nonlinear aeroelastic equations for combined flapwise bending, chordwise bending, torsion, and extension of twisted nonuniform rotor blades in forward flight

摘要

The second-degree nonlinear aeroelastic equations for a flexible, twisted, nonuniform rotor blade which is undergoing combined flapwise bending, chordwise bending, torsion, and extension in forward flight are developed using Hamilton's principle. The equations have their basis in the geometric nonlinear theory of elasticity and are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity, and the square of the derivative of the extensional deformation of the elastic axis is negligible compared to the squares of the bending slopes. No assumption is made regarding the coincidence of the elastic, mass, and tension axes of the blade, although the elastic and aerodynamic center axes are assumed coincident at the blade quarter chord. The blade aerodynamic loading is obtained from strip theory based on a quasi-steady approximation of two-dimensional, incompressible unsteady airfoil theory. The resulting equations are compared with several of those existing in the literature. These comparisons indicate several discrepancies with the present equations, particularly in the nonlinear terms. The reasons for these discrepancies are explained.