Sensitivity Analysis and Optimization of High-Aspect-Ratio Wings with Respect to Mass and Stiffness Distributions

High-aspect-ratio wings improve aerodynamic efficiency but suffer from greater gust-induced loads, requiring innovative design methods for gust load alleviation (GLA). This study develops a reduced-order aeroelastic model to enable efficient sensitivity analysis and optimization of structural properties for passive GLA in the early design stage. A beam-based structural model was coupled with unsteady potential-flow aerodynamics in the frequency domain. The formulation, implemented in JAX, exploits automatic differentiation (AD) to compute gradients of gust responses with respect to spanwise mass and stiffness distributions. Validation was performed against MSC Nastran results. The model reproduced static and dynamic aeroelastic responses within ~10% error rate compared to MSC Nastran. Sensitivity analyses revealed that the influence of structural properties strongly depends on the chosen objective function, with mass and elastic axis location showing notable but sometimes conflicting trends. Gradient-based optimization demonstrated improved load alleviation but highlighted risks of overfitting to specific gust profiles. The proposed framework enables scalable, differentiable optimization of gust responses, bridging microstructural design and aeroelastic performance. These findings indicate that the proposed differentiable framework constitutes a valuable methodology for early-stage design, offering an efficient means to couple aeroelastic performance with structural optimization.