Nonlinear Dynamics

, Volume 78, Issue 4, pp 2399–2408 | Cite as

Effect of the aerodynamic-induced parametric excitation on the longitudinal stability of hovering MAVs/insects

  • Haithem E. Taha
  • Ali H. Nayfeh
  • Muhammad R. Hajj
Original Paper


Longitudinal flight dynamics of hovering micro-air-vehicles and insects is considered. The natural oscillatory flapping motion of the wing leads to time-periodic stability derivatives (aerodynamic loads due to perturbation in the body-motion variables). Hence these terms play the role of parametric excitation on the flight dynamics. The main objective of this work is to assess the effects of these aerodynamic-induced parametric excitation terms that are neglected by the averaging analysis. The method of multiple scales is used to determine a second-order uniform expansion for the response of the time-periodic system at hand. The proposed approach is applied to the hovering flight dynamics of five insects that cover a wide range of operating frequency ratios to assess the applicability of the averaging analysis.


Flapping flight Hovering insects Micro air vehicles Time-periodic systems Perturbation techniques Method of multiple scales Flight dynamics Averaging theorem Parametric excitation 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Haithem E. Taha
    • 1
  • Ali H. Nayfeh
    • 1
    • 2
  • Muhammad R. Hajj
    • 1
  1. 1.Virginia TechBlacksburgUSA
  2. 2.University of JordanAmmanJordan

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