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, are all demonstrated via gradient-based optimization.