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Fractional order derivative aero-servo-viscoelasticity

Article

Abstract

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.

Keywords

Aero-servo-viscoelasticity Controls Coupled systems Divergence Flutter Fractional derivatives Integer derivatives Nyquist diagrams Prony series 

Notes

Acknowledgments

Support by grants from the Private Sector Program Division (PSP) of the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign (UIUC) and from the Mechanical and Aerospace Engineering Department at Carleton University is gratefully acknowledged.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Mechanical and Aerospace Engineering DepartmentCarleton UniversityOttawaCanada
  2. 2.Aerospace Engineering Department, College of Engineering, Private Sector Program Division, National Center for Supercomputing ApplicationsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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