Stability and power optimality in time-periodic flapping wing structures |
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| Affiliation: | 1. U.S. Air Force Research Laboratory, Wright-Patterson AFB, Dayton, OH 45433, USA;1. Department of Structural and Geotechincal Engineering, Sapienza University of Rome, Via A. Gramsci 53, 00197 Rome, Italy;2. Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy;1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FI-40014, Finland;2. Institute for Problems in Mechanics RAS, Prospect Vernadskogo 101, Bld. 1, 119526 Moscow, Russian Federation |
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| Abstract: | This paper investigates the nonlinear dynamics of a vehicle with two flexible flapping wings. The body dynamics and the wings’ deformation are monolithically grouped into a single system of equations, with aerodynamics accounted for by a quasi-steady blade element method. A periodic shooting method is then used to locate closed orbits of this non-autonomous system, and Floquet multipliers assess the linearized stability about the nonlinear orbit. This framework is then exposed to a gradient based optimizer, in order to quantify the role of wing planform variables, wing structure variables, and kinematic actuation variables in obtaining vehicles with superior open-loop stability characteristics, and/or low-power requirements. |
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