Simplified integrated model of the flight dynamics of flexible aircraft

Resumo

© 2025 Elsevier Masson SASA simplified integrated model of the flight dynamics of flexible aircraft is developed using the Rayleigh-Ritz and quasi-steady vortex-lattice methods. In a novel approach, the Rayleigh-Ritz method is applied to all structural components with the inclusion of six rigid-body shape functions per component, allowing the enforcement of compatibility conditions between components and the calculation of modes of vibration for the entire aircraft at once. Another novelty is that, although aerodynamic influence coefficient matrices are calculated only for the jig shape, the vortex-lattice method boundary conditions and force equations are implemented in vector form and updated throughout flight simulations, allowing the formulation to capture important nonlinear aerodynamic effects related, e.g., to angular velocities, follower forces due to wing dihedral deformation, and induced drag. The equations of motion consider mean axes and a set of unrestrained modes of vibration. For simplicity, beam-like components with small deformations are considered. Using quasi-steady aerodynamics avoids the greater unsteady aerodynamic model preparation effort and computational cost. These characteristics make the proposed integrated model potentially useful in the initial stages of aircraft design when unifying aeroelasticity and flight dynamics is mandatory, as is the case for next-generation commercial aircraft. Convergence in the Rayleigh-Ritz method is achieved by varying the number of shape functions and its application to an aircraft comprising 20 beams shows that, compared to a model with 3006 degrees of freedom, one with only 606 results in frequency errors of less than 4% for all modes below 25 Hertz. Applying the framework to aircraft with decreasing stiffness levels reveals important phenomena, such as reduced short-period mode damping and frequency, increased damping of wing bending aeroelastic modes, and increased susceptibility to aileron roll control reversal.

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