USE OF HIERARCHICAL ELASTIC BLADE EQUATIONS AND AUTOMATIC TRIM FOR HELICOPTER VIBRATION ANALYSIS

A unified approach has been developed to obtain the elastic blade equations in forward flight, when a blade undergoes flap, lag, and torsional motions. The mathematical model used in this analysis includes a tensor approach for strain components, a curvilinear coordinate system, a new and consistent ordering scheme, modified Greenberg's aerodynamic theory, and an optimized automatic controller for trim settings. These are the vital building blocks used to obtain the equations of motion. Although some of these features are found in the literature piecewise, the present analysis brings all of them together under one unified umbrella. The hierarchical nature of the elastic blade equations leads to the possibility of reducing them to various orders. A new family of orthogonal polynomials is developed for the purpose of applying a Galerkin time-history solution. The results show that this is a viable approach.