Modeling and analysis of the flight dynamics of a deformable aircraft with structurally-linearized full inertial coupling

Abstract

Aeronautical engineering has faced a significant and continued development over the last decades towards the design of lighter, more maneuverable and more multidisciplinarily optimized aircraft, leading to more flexible vehicles. In this context, the fields of aeroelasticity and aeroservoelasticity play a very important and increasing role. Neglecting such flexibility effects on the flight dynamics and control system analysis and design may be an invalid premise, depending on how intense might be the coupling between the rigid and the flexible degrees of freedom. Traditional modeling approaches have often neglected the effects of inertial coupling in the treatment of the dynamics of the deformable aircraft, allowing great simplifications of the equations of motion. Most authors have indeed considered the body axes to be mean axes, what requires some care regarding the enforcement of the correct constraints and the expression of the aerodynamic force components along these axes directions. Looking for circumventing those limitations, while keeping the hypothesis of small local deformations, this work presents an integrated modeling methodology for the flight dynamics of deformable aircraft which takes into account all the coupled dynamics and is based on attached body axes. The formulation is developed for direct use with a finite-element model of the aircraft structure, with known distributed or lumped mass properties. The nonlinear inertial coupling terms are linearized with respect to the linear elastic displacements around an equilibrium condition. This condition is determined with the full nonlinear dynamics, considering displacement and load-transferal between the aerodynamic model and the finite-element model. Inertia-relieved constrained modes of vibration are then used as shape functions in the calculation of the dynamic deformation of the structure, thus not canceling the inertial coupling terms as would happen in the case of free-free normal modes. The proposed formulation is implemented and tested for simulating the flight of a generic narrow-body airliner (GNBA) model which has been developed for the purpose of these studies. The aerodynamic forces and moments are treated as the superposition of two contributions: the expected rigid-body ones and the incremental ones due to the structural deformation. The incremental aerodynamic forces and moments are modeled by the doubletlattice method (DLM). Rational-function approximation (RFA) together with the method of least squares for complex variables to determine the coefficients of the RFA and inverse Laplace transforms are employed to represent the reduced-frequency-domain forces in the time domain, leading to an augmented state-space system in which the aerodynamic lag phenomenon is taken into account.

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