| A stability analysis has been developed for a hingeless, composite, isolated rotor in hover. The analysis is a finite element based solution of mixed, weak, intrinsic dynamic equations for a rotating beam. The aerodynamic forces were modeled with two-dimensional, quasi-steady strip theory, with inflow taken from momentum/blade element theory.;The completely nonlinear analysis includes shear deformation, a mechanism for the inclusion of a complete 6 x 6 stiffness matrix (relating six generalized forces and moments to six generalized strains and elastic curvatures), and the effects of rotary inertia. In other words, the analysis can handle nonclassical couplings as well as shear deformation. In addition, no explicit restrictions on the magnitudes of the displacement and rotation components were made; the only implicit restriction was that the magnitudes of the strain components remain small compared to unity.;The blade's equilibrium position was obtained by an iterative solution of the complete nonlinear equations using the Newton-Raphson method. The dynamic equations were linearized about this position and a small motion solution to the resulting eigen-problem was obtained. The eigenvalues give the damping and frequency of each eigenvector.;The resultant FORTRAN program was thoroughly validated against analytical and existing experimental results for equilibrium, dynamic, and stability calculations. The validations encompassed both small and large equilibrium deflections. In addition, extensive correlations were performed against experimental composite results, including both static and dynamic cases. These studies indicate that the current approach accurately represents large deflections and linearized dynamics and is capable of predicting composite behavior quite well.;The accuracy of the composite predictions was found to depend on the quality of the cross-sectional stiffnesses. The two-dimensional analyses used, however, gave nearly identical results for many cases because of their high quality. The performance of the "classical" stiffnesses (which ignore shear deformation effects), however, was poor for several cases. The stability cases studied were not typically very sensitive to the nonclassical couplings. There was one stability case, however, for which a significant error appeared (especially at high thrust levels) when bending-shear coupling was neglected. |
