Analytical model and stability analysis of the leading edge spar of a passively morphing ornithopter wing.
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.
University of Illinois at Urbana Champaign, 1206 West Green Street, Urbana, IL 61801, USA.
Aimy
A
Wissa
Joseph
J
Calogero
Norman
N
Wereley
James E
JE
Hubbard
Mary
M
Frecker
D000401:Aircraft / Q000295:instrumentation*; D000818:Animals; D001717:Birds / Q000502:physiology*; D017076:Computer-Aided Design; D055119:Elastic Modulus / Q000502:physiology; D004867:Equipment Design; D019544:Equipment Failure Analysis; D005426:Flight, Animal / Q000502:physiology*; D008954:Models, Biological; D009024:Morphogenesis / Q000502:physiology; D012212:Rheology / Q000379:methods; D012371:Robotics / Q000295:instrumentation*; D014921:Wings, Animal / Q000502:physiology*