# Aeroelastic Loads Modeling for Composite Aircraft Design Support

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## Abstract

With regard to the simulation of structural vibrations and consequent aeroelastic loads in aircraft components, the use of elastic axis e.a as reference of vibrations is quite common. The e.a decouples the bending and torsion degrees of freedom (D.o.F) during the dynamic analysis. The use of the e.a to decouple the bending and torsion in vibration analysis does not work for fiber composite structures with anisotropic material properties. Anisotropic material properties often result in an elastic axis that is either discontinuous or far outside the real aircraft. Existing mathematical models of exible aircraft dynamics do not address this issue. In this report, state of the art inertially coupled equations of motion of a flexible aircraft are modified. For each of the equivalent beam model of the fuselage, wings, and tail structure a particular fixed reference axis r.a is used for vibrations instead of elastic axis. Since no decoupling can be used, the beam deflections become a function of both bending and twist. The resulting displacements are expanded to the expressions of beam generalized velocities. Apart from the inclusion of the coupling effects, it is also thought to modify the structural dynamics model that, apart from the conventional tail configuration, should also accommodate the analysis of T-Tail configuration aircraft. These developments modify the expressions of kinetic and strain energies and subsequent global mass and stiffness matrices, state-space coeffcient matrices. The modified model is then linearized into zero-order problem (i.e. rigid-body maneuvers) and first-order problem (i.e. vibrations and their effects on the rigid-body response of the aircraft). The equations of motion are then expanded to the structural loads equations, which are based on the summation of forces method (SFM) and mode displacement method (MDM). SFM is based on the summation of all the aerodynamic, gravity, and inertial forces on a component. Whereas the MDM is based on the structural deformations caused by the external forces. The results computed from SFM can be verified by comparing to those of the results from the MDM. A computer code, DARLoads, is written to simulate the dynamics of the flexible aircraft and all the equations given in this report are programmed in MATLAB software. An executive twin-jet is selected for the simulation. Due to the nonavailability of the composite aircraft data the coupling effects on the response of the aircraft are studied by manipulating the e.a of each wing and horizontal tail of the metal aircraft in five different cases of numerical examples. In first three cases, the e.a of each wing and horizontal tail is drawn parallel to the r.a of that particular component, where the e.a with respect to r.a of each component is placed in three different positions. In the fourth and fifth case, the e.a of each wing and tail is drawn by intersecting the shear centers of each section from root to tip. The aircraft is trimmed at the given air speed and altitude for each e.a case, which shows that the coupling affects the trim variables significantly (i.e. elevator and thrust inputs, and the pitch angle) and moreover the static deflections. For each optimized trim condition the aircraft is subjected to different dynamic conditions, which include the discrete gust and abrupt checked elevator maneuver with a conventional tail configuration, and impulse aileron input with a T-tail configuration. The results in the form of rigid-body response and consequent structural loads show the same kind of scenario as observed in the static case (i.e. during trim solution). It shows that the position of elastic axis has significant effects on the dynamics of the fully flexible composite aircraft.