A state-space airloads theory for flexible airfoils

In this paper, classical thin airfoil theory is extended in four ways. First, the theory is reformulated to apply to an airfoil that is performing large frame motions with respect to the air mass. Second, airfoil motions within the frame are allowed to include completely general dynamic deformations of the cross-section. Third, the theory is formulated in terms of generalized deflections and generalized forces within that frame, which leads to mass, damping, and stiffness matrices for the generalized airfoil motion. Fourth, although most of the applications herein are in the context of a two-dimensional flat wake in the frequency domain (as in Theodorsen theory), the theory is cast such that it can be coupled with any unsteady wake model desired, including three-dimensional wake models such as vortex-lattice. Comparisons with other theories will show that this new theory includes the classical theories of Wagner, Theodorsen, Garrick, Loewy, Greenberg, and Isaacs when applied to those special cases.