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Open Access Publications from the University of California

The need for higher-order averaging in the stability analysis of hovering, flapping-wing flight.

  • Author(s): Taha, Haithem E
  • Tahmasian, Sevak
  • Woolsey, Craig A
  • Nayfeh, Ali H
  • Hajj, Muhammad R
  • et al.

Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.

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