Stability analysis for design improvement of bio-inspired flapping wings by energy method

Abstract

This study attempts to reach a broad understanding of the stability properties of nonlinear time-periodic flapping wing structures. Two bio-system models, Hummingbird (6DOF) and Hawkmoth (3DOF) are developed for this purpose. Initial analysis on the Hummingbird model, which is based on the Floquet theory, kinetic energy integration, and phase portrait technique, indicates lack of stability in hover flight. Kinetic energy integration is carried out on the extended model of the Hawkmoth to find the domain of attraction and increase the level of stability by varying the design parameters. Here, the hinge location of the wing, flapping amplitude, flapping frequency, and mean angle of attack are adjusted to achieve steady hovering trim condition. The results will be used for hovering control design that is a problem with no clear solution and has been widely studied based on linear analysis and averaging theory regardless of the stability properties. In addition, by averaging theory and linearization technique, the range of mean angle of attack that is associated with the pitch angle is also determined by using eigenvalues to achieve dynamic stability for further nonlinear analysis. Sensitivity analysis is then performed with the phase portrait and energy approach on the equivalent dynamics to reach the main cause of instability. Improved parameters are applied to the non-autonomous dynamics, and for the first time, the creation of a strange attractor is observed in three-dimensional phase space by Floquet analysis.