Stability Analysis of the Wing Leading Edge Spar of a Passively Morphing Ornithopter

Abstract

This paper presents a stability model for the wing leading edge spar of a test ornithopter. The long-term goal of this research effort is to passively improve the performance of ornithopters during steady level flight by implementing a set of wing kinematics found in natural flyers. The desired kinematics is achieved by inserting a compliant mechanism called a compliant spine into the wing leading edge spar to mimic the function of an avian wrist. The stiffness of the compliant spine is time varying and given the nature of flapping flight, it is periodic. Introducing a variable stiffness compliant mechanism into the leading edge spar of the ornithopter affects its structural stability. Therefore, a stability analysis is required. In order to start the stability analysis, an analytical model of the ornithopter wing leading edge spar with a compliant spine inserted in is necessary. In the model, the compliant spine is modeled as a torsional spring with a sinusoidal stiffness function. Moreover, the equations of motion of the wing leading edge spar-spine system can be written in the form of non-homogeneous Mathieu’s equations, which has well-known stability criteria. The analytical system response is then validated using experimental data taken at NASA Langley Research Center. Results show that the analytical spine angular deflection agrees with the experimental angular deflection data within 11%. Stability was then demonstrated using both analytical and graphical proving that the response of leading edge spar with a compliant spine design inserted at 37% of the wing half span is bounded.