Nonlinear aeroelasticity of high-aspect-ratio wings with laminated composite spar

The aeroelastic instability of a high-aspect-ratio wing including anisotropic composite wing–spar in an incompressible flow is investigated. Combining a nonlinear Euler–Bernoulli beam theory and a composite laminate theory, the third-order expansion of nonlinear structural equations of motion and associated boundary conditions are obtained for vertical, forward/afterward, and torsional motion of the high-aspect-ratio composite wing undergoing large deformations and small strains, neglecting warping, shear deformation, and small Poisson effects. The unsteady aerodynamic strip theory based on Wagner’s function is used for determining the aerodynamic loading of the wing. Combining these two sets of equations gives a set of nonlinear integro-differential aeroelastic equations of motion. The governing partial differential equations are discretized using Galerkin’s method, and the obtained equations are solved with a numerical method with no need to add any aerodynamic state-space degrees of freedom. Some test cases are analyzed and the results are evaluated based on the results given in other references. Also, a study is conducted to show the effects of fiber orientation variations on nonlinear aeroelastic instability speed and nonlinear aeroelastic instability frequency of the composite wing. The study shows that fiber orientation strongly affects the aeroelastic characteristics of a non-isotropic wing where the aeroelastic instability speed dominantly decreases for the fiber orientation between − 90° and  − 45° or 0° and  + 45°. It is also shown that in the fiber orientation between − 45° and  + 45°, the bending–bending stiffness and in the other fiber orientation, the bending–torsion coupling stiffness have a significant role in decreasing or increasing the nonlinear instability speed of the wing.