On the Influence of Planform Geometry and Aspect Ratio on Aeroelastic Flutter Boundaries in Rigid and Flexible Aircraft Wings

Flutter constrains the design of modern high-aspect-ratio wings, yet the combined influence of planform geometry, aspect ratio (AR) and structural flexibility is rarely assessed within a single consistent framework. This work presents a unified, physics-based reduced-order comparison of rectangular, trapezoidal and elliptical planforms under both rigid and flexible representations, intended as a screening tool for preliminary design rather than as a quantitatively predictive methodology for specific aircraft. A two-degree-of-freedom plunge–pitch typical section with quasi-steady (Theodorsen-based) aerodynamics is cast in state-space form, and flutter is identified through eigenvalue continuation by combined frequency coalescence and damping sign change. For rectangular and trapezoidal wings, increasing AR or reducing stiffness consistently advances flutter onset: at a fixed AR of 7.1, stiffening alone raises the critical speed by approximately 43 m/s (from 105 to 148 m/s, ≈+41%). In contrast, within the reduced-order model the elliptical planform inverts this trend: with sufficient stiffness, frequency coalescence is suppressed, and from the stiffened baseline (AR ≈ 4.75) raising AR to 5.6 keeps the wing flutter-free across the investigated velocity range, whereas lowering AR to 3.9 reintroduces hard flutter at 155 m/s. These model-based comparative tendencies indicate that AR and structural flexibility are strongly coupled design drivers and that elliptical loading is comparatively flutter-resistant, providing an efficient basis for early-stage configuration screening.