Bifurcation-Diagram-Free Postflutter Response Constraint for Design Optimization

Abstract

This paper introduces a new metric to constrain postflutter responses of aeroelastic systems in design optimization. The new metric aggregates the recovery rate to equilibrium for a range of operating conditions, modes, and amplitudes, resulting in a scalar constraint that does not involve the bifurcation diagram. By generalizing damping-based flutter constraints, the formulation yields mathematical properties oriented toward gradient-based optimization. The approach is demonstrated by optimizing a typical section with a subcritical bifurcation using a gradient-based algorithm and finite-difference derivatives. The postflutter response constraint suppresses self-sustained oscillations below a given flow speed while minimizing the mass penalty, which avoids a conservative solution. This constraint can help design highly efficient aeroelastic systems with feasible postflutter dynamics. Future development of adjoint derivatives will enable large-scale gradient-based optimization.