Analytical model and stability analysis of the leading edge spar of a passively morphing ornithopter wing

Aimy Wissa, Joseph Calogero, Norman Wereley, James E. Hubbard, Mary I. Frecker

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

This paper presents the stability analysis of the leading edge spar of a flapping wing unmanned air vehicle with a compliant spine inserted in it. The compliant spine is a mechanism that was designed to be flexible during the upstroke and stiff during the downstroke. Inserting a variable stiffness mechanism into the leading edge spar affects its structural stability. The model for the spar-spine system was formulated in terms of the well-known Mathieu's equation, in which the compliant spine was modeled as a torsional spring with a sinusoidal stiffness function. Experimental data was used to validate the model and results show agreement within 11%. The structural stability of the leading edge spar-spine system was determined analytically and graphically using a phase plane plot and Strutt diagrams. Lastly, a torsional viscous damper was added to the leading edge spar-spine model to investigate the effect of damping on stability. Results show that for the un-damped case, the leading edge spar-spine response was stable and bounded; however, there were areas of instability that appear for a range of spine upstroke and downstroke stiffnesses. Results also show that there exist a damping ratio between 0.2 and 0.5, for which the leading edge spar-spine system was stable for all values of spine upstroke and downstroke stiffnesses.

Original languageEnglish (US)
Article number065003
JournalBioinspiration and Biomimetics
Volume10
Issue number6
DOIs
StatePublished - Oct 26 2015

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Biophysics
  • Biochemistry
  • Molecular Medicine
  • Engineering (miscellaneous)

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