This paper elaborates on the theoretical development of a mathematical approach, targeting the real-time simulation of aero-elasticity for open rotors with slender blades, as employed in the majority of rotorcraft. A Lagrangian approach is formulated for the rapid estimation of natural vibration characteristics of rotor blades with nonuniform structural properties. Modal characteristics obtained from classical vibration analysis methods are utilized as assumed deformation functions. Closed form integral expressions are incorporated, describing the generalized centrifugal forces and moments acting on the blade. The treatment of three-dimensional elastic blade kinematics in the time-domain is thoroughly discussed. In order to ensure robustness and establish applicability in real time, a novel, second-order accurate, finite-difference scheme is utilized for the temporal discretization of elastic blade motion. The developed mathematical approach is coupled with a finite-state induced flow model, an unsteady blade element aerodynamics model, and a dynamic wake distortion model. The combined formulation is implemented in an existing helicopter flight mechanics code. The aero-elastic behavior of a full-scale hingeless helicopter rotor has been investigated. Results are presented in terms of rotor blade resonant frequencies, rotor trim performance, oscillatory structural blade loads, and transient rotor response to control inputs. Extensive comparisons are carried out with wind tunnel (WT) and flight test (FT) measurements found in the open literature as well as with nonreal-time comprehensive analysis methods. It is shown that the proposed approach exhibits good agreement with measured data regarding trim performance and transient rotor response characteristics. Accurate estimation of structural blade loads is demonstrated, in terms of both amplitude and phase, up to the third harmonic component of oscillatory loading. It is shown that the developed model can be utilized for real-time simulation on a modern personal computer. The proposed methodology essentially constitutes an enabling technology for the multidisciplinary design of rotorcraft, when a compromise between simulation fidelity and computational efficiency has to be sought for in the process of model development.

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