Assessment of static divergence and flutter characteristics for a canonical geometry

Abstract

Aeroelastic instabilities such as static divergence and flutter represent first-order design constraints for any lifting surface, since they may lead to a sudden and catastrophic loss of structural integrity. Their early prediction is therefore essential during wind-tunnel model design, structural sizing, instrumentation integration and flutter-clearance activities. The present work proposes a reduced-order aeroelastic framework that combines structural quantities extracted from a finite-element model (FEM) with a generalized-coordinate reduction to two degrees of freedom — one bending and one torsion — and with classical aeroelastic theory. A sequence of static FEM analyses under unit loads is used to locate the elastic axis, to assemble the generalized compliance and stiffness matrices and to project the structural mass matrix onto the generalized coordinates. Static divergence is then obtained as a real generalized eigenvalue problem, whereas flutter is formulated through Theodorsen’s unsteady thin-airfoil theory and solved as a complex eigenvalue problem in which the real and imaginary parts of the aeroelastic determinant are driven simultaneously to zero. The methodology is applied to the canonical Goland wing and assessed against a consolidated set of published benchmark results which exhibit a considerable dispersion — reported flutter speeds range from roughly 130 to 165 m/s depending mainly on the dimensionality of the aerodynamic model. Within this context, the framework recovers the dominant bending–torsion coupling and yields divergence and flutter speeds of the physically consistent range; for the Goland test case the predicted flutter speed lies below the divergence speed, so that the configuration is flutter-critical. The proposed approach provides a coherent and computationally inexpensive basis for preliminary aeroelastic stability assessment.