Topology optimization is a procedure focused on enhancing the structural efficiency of a design subject to physical constraints such as mass, stress, deflection, and frequency. This work focuses on a SIMP-based topology optimization procedure for designing a passively actuated bistable airfoil that utilizes buckling-induced snap-through and variable support locations to achieve stable configurations under prescribed flight conditions. We couple nonlinear finite element analysis with an arc-length solver [1,4] to capture large structural deformations and post-buckling behavior needed for accurate modeling of the snap-through response, and use the Method of Moving Asymptotes [2] as our optimizer. Super-Gaussian function parameterization [3,4] is also employed to optimally distribute the structural supports and facilitate the layout of internal snap regions that can encourage or prevent buckling transitions. We use a smooth and differentiable Kreisselmeier–Steinhauser (KS) aggregation function to identify the lowest natural frequency and account for eigenmode crossover. Additionally, we compute frequency constraint sensitivities using an adjoint-based method. Our approach diverges from traditional methods by allowing flexibility in the placement of supports while keeping the aerodynamic load distribution fixed. In this way, we can optimize support locations concurrently with the internal airfoil structure, thereby improving the design's structural and aerodynamic performance. This is a procedure that co‑optimizes topology, movable supports, and a graded skin while respecting a minimum eigenfrequency. The scheme remains fully differentiable and requires no mode‑tracking. Numerical examples demonstrate the benefits of jointly considering mass, frequency, and aerodynamic constraints when designing airfoil structures with variable support locations. The study's outcomes illuminate the potential of this integrated approach in topology optimization, especially for morphing airfoils and other structures where aerodynamic performance is as crucial as structural integrity.