Fixed- and Free-Mode Flutter Derivatives During Aeroelastic Optimization

Aeroelastic flutter design derivatives may be approximated by ignoring the sensitivity of the structural mode shapes. This fixed-mode derivative is less expensive to compute than the exact free-mode derivative (which accommodates the mode shape dependency) but also may provide inaccurate sensitivities for optimization. This work formulates both fixed- and free-mode flutter derivatives and demonstrates the conditions under which they are equivalent. Two different types of fixed-mode derivatives are also developed in this work. Using a cantilevered-plate demonstration problem with both shape and sizing design parameters, the accuracy of the free-mode derivative and the two fixed-mode derivatives is demonstrated via gradient-based optimization.