Elastodynaimc Systems: Ornithopters And Power Harvesting

Abstract

Ornithopters are air vehicles that fly using flapping wings as lift and propulsion. The study of ornithopter flight dynamics is complicated by time-varying aerodynamics and no dynamic steady state. Using quasi-steady aerodynamics, a Newton-Euler dynamic model of ornithopter flight is utilized to study ornithopter stability and flight dynamics. Floquet analysis is used to analyze these periodic steady flight regimes. This model is then used to analyze and synthesize stabilizing controllers for forward flight and hovering flight. A novel controller is a discrete-time periodic linear quadratic regulator, useful for steady periodic flight dynamics. The model is exploited further to analyze and optimize a nonsteady maneuver: to connect forward flight to hovering flight midflight. Finally, an ornithoptic dirigible is designed and constructed in order to study flapping-wing flight dynamics without requiring the wings to provide lift. The blimp's dynamic modes are observed using a motion capture system. Energy harvesting using cantilevered piezoelectric bimorph vibrators has potential to generate power for long-endurance, low power devices. The geometry of these bimorph vibrators is modeled using Euler-Bernoulli vibration models and the width profile is optimized to produce the highest power transduction. It is found that beams tapering toward the tip are capable of withstanding higher strain, and thus can be subject to stronger vibration at a smaller mass. The Timoshenko model of piezoelectric beam vibration is then derived and compared to the Euler-Bernoulli model and found to be more accurate at higher frequencies and at lower length-to-width ratios.