A coupled rotor-fuselage aeroelastic analysis using complex rotor modes
A new modal method capable of analysing the aeroelastic response of rotorcraft in both steady and manoeuvring flight is developed. Particular emphasis is given to the correct modelling of the dynamic interactions between the rotor and the fuselage. This is achieved via the use of complex rotor modes, which allows the effects of hub motion to be incorporated. The modal Lagrangian equation for a single rotating blade using real modes as state variables is first derived. The important non-linear terms based on an ordering scheme are retained. This aeroelastic model is then extended to adopt the complex rotor modes as state variables. This concept, which is both new and analytically demanding, is furnished with minimum algebra. A generalised proof of complex modes orthogonality and its application to the coupled rotor-fuselage dynamic system are provided. Important conclusions drawn from this proof include: A set of complex left-hand eigenvectors are required, together with the right-hand set, in order to reduce the system response equations to an uncoupled modal form suitable for a solution; and It is necessary for the modes analysis to be re-formulated as an eigenvalue problem replacing the transfer matrix solution procedure. An orthogonalisation procedure is employed to reduce the complex system response equations to the uncoupled modal form. The procedure not only simplifies the algebraic process, but also identifies exactly the forcing functions present in the dynamic system modelled. However, for consistency wi th the dynamic model, it is necessary to restrict the blade model to a straight beam with small pre-deformed angles. The need to treat both the complex coupled and reactionless mode sets simultaneously, when they are defined in different reference frames, requires special attention to the solution of the modal responses. A numerical technique is developed for filtering the applied forces and hence identifying the forcing for the respective mode types. The fundamental issue regarding the true definition of angle of attack used for aerodynamic calculation is also addressed. The second order pseudo-torsion term must be removed from the incidence expression to ensure the aerodynamic loads are calculated correctly. The determination of the blade structural loads using both Modal Summation and Force Integration methods is discussed and described. A novel numerical technique, based on curve fitting using Chebyshev polynomials coupled with analytical integration, is devised and shown for the first time to minimise the inherent numerical problems associated with Force Integration. Finally, applications of the analytical model to include the effects of hub motion on vibratory loads calculation and to determine loads in an extreme manoeuvre are successfully demonstrated. The use of rotor modes by including transmission flexibility in a rotor dynamic model in loads calculation is also provided. These correlations establish the important milestone on the ability of this model to improve vibration prediction and to simulate manoeuvring flight. They also demonstrate the potential applications of this model. Recommendations for future research are also made.