Linearization and Analytical Sensitivity of Unsteady Vortex-Lattice Aerodynamics

The unsteady vortex-lattice method (UVLM) provides a high-efficient, medium-fidelity way to capture large deformations and free wake effects of flexible wings. It has been favored in research on the stability analysis of flexible wings. It is possible to construct linearized aeroelastic equations and improve the efficiency of dynamic stability analysis, by applying linearized governing equations based on the assumption of small disturbances and analytical aerodynamic sensitivities based on the chain rule. The linearized governing equations and analytical sensitivities of UVLM can also be applied to aeroelastic control and optimization design. Numerical simulations show that aerodynamic loads are more sensitive to the normal component of node displacement. Analytical sensitivities are validated to be accurate and more efficient than finite difference methods.