Analytical model and stability analysis of the leading edge spar of a passively morphing ornithopter wing. (26th October 2015)

• Record Type: Journal Article
• Authors: Wissa, Aimy; Calogero, Joseph; Wereley, Norman; Hubbard, James E; Frecker, Mary
• Is Part Of: Bioinspiration & biomimetics. Volume 10:Number 6(2015:Dec.)
• Publication Date: 2015-10-26
• Subjects: ornithopter -- stability analysis -- linear time periodic model -- Mathieu's equation; Biomimetics -- Periodicals; Biomedical materials -- Periodicals; Medical innovations -- Periodicals; Biomedical engineering -- Periodicals; 600
• DOI: 10.1088/1748-3190/10/6/065003
• Languages: English
• ISSNs: 1748-3182

Abstract

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.