Discrete Bar-Chain Model for Aeroelastic Stability Analyses of Flexible Slender Thin Wings in Subsonic Flow at Low Speed

A novel semi-analytical computational approach is formulated and assessed for the dynamic aeroelastic stability analysis of flexible slender thin wings in incompressible flow, which can boost the preliminary airframe design and optimisation of lightweight aircraft, offering both theoretical and practical insights. Hencky’s bar-chain model is explicitly adopted as a discrete numerical implementation of the Euler–Bernoulli continuous beam idealisation for the flexible wing structure and its deformation, resulting in a linear system of coupled ordinary differential equations for its bending and torsion dynamics. Modified strip theory is employed for the unsteady sectional airload, where approximate yet effective analytical expressions are efficiently adopted for its build-up and distribution, combining two- and three-dimensional effects in subsonic potential flow. Once the natural vibration modes of the wing are obtained from its physical model, a reduced set is selected, and a modal approach is then employed to perform its aeroelastic stability analysis with either “p-k” or “p” method, depending on the aerodynamic model. Numerical results from such a reduced-order model are critically assessed for the flutter analysis of Goland’s, Loring’s, and Pazy wings and demonstrate excellent agreement with literature results for two- and three-dimensional airflow, also for the case of the swept wing.