Stability and Dynamic Response Analysis of Rotating Blades Using Fully Intrinsic Equations

As part of an ongoing investigation into potential advantages of so-called fully intrinsic formulations, this paper presents the fully intrinsic equations of motion and kinematics for beams. A fully intrinsic formulation is devoid of displacement and rotation variables and, although they are geometrically exact, they are free of the attendant singularities and infinite-degree nonlinearities found in other types of formulations. These nonlinear, first-order partial differential equations are suitable for analyzing initially curved and twisted, anisotropic beams and are very attractive for analysis of both helicopter and wind turbine rotors. Application of these equations to the modeling of rotor blades is undertaken for a wide variety of boundary conditions, in particular the modeling of hingeless and bearingless rotor configurations. Results obtained are presented and compared with those obtained from DYMORE for verification purposes.