Z-Fold Wing Aeroelasticity: Compositional Modeling, 1:2 Double-Hopf Dynamics, and Nonlinear Stiffness Effects

Abstract

Folding changes the linearized aeroelastic spectrum and can switch which mode becomes unstable first, with consequences for local postflutter interactions. This study formulates a three-component Z-fold wing by assigning every aerodynamic station to a structural component and a material coordinate. The same attachment map generates surface motion and returns pressure loads through virtual work. Geometrically exact component dynamics, an explicit-wake unsteady vortex-lattice model, and block-structured descriptor assembly preserve the physical paths of configuration actions. A two-parameter flutter analysis shows that a smooth flutter-speed envelope conceals a high-low-high sequence of controlling neutral branches, expressed as a critical-frequency valley and a redistribution of component deformation. Numerical continuation locates a near-1:2 double-Hopf point. Within a local model retaining quadratic and cubic structural restoring forces with aerodynamic and inertial operators fixed at the scheduling point, the cubic normal form captures selected 26-state observations and admits high-frequency-dominant and mixed phase-locked periodic solutions. The formulation links configuration-dependent flutter-mode identity to local resonant dynamics and supports blockwise sensitivity and design reasoning.