Fractional order derivative aero-servo-viscoelasticity

Divergence and flutter of lifting surfaces obeying fractional derivative (FD) viscoelastic material constitutive relations under separate fractional derivative servo-controls are analytically investigated. The analytical and computational complexities of FD formulations are examined and compared to Prony series formulations, which are the equivalent of integer derivative viscoelastic characterizations. An approximate formulation is offered that facilitates the Fourier transform but not the evaluation of the convolution integrals. Stability in the form flutter and torsional divergence of a two DOF system is investigated in the Laplace transform space by modified Nyquist plots. Illustrative examples demonstrate that the use of Prony series modulus/compliance characterizations offers a much simpler path to stability determinations in real time than the quest for intersections of curves of flight speeds and frequencies associated with fractional derivative representations.