Effects of structural flexibility of wings in flapping flight of butterfly

The objective of this paper is to clarify the principle of stabilization in flapping-ofwings flight of a butterfly, which is rhythmic and cyclic motion. For this purpose, a dynamics model of a butterfly is derived by Lagrange´s method, where the butterfly is considered as a rigid multi-body system. For the aerodynamic forces, a panel method is applied. Validity of the mathematical models is shown by agreement of the numerical result with the measured data. Then, periodic orbits of flapping-of-wings flights are searched in order to fly the butterfly models. Almost periodic orbits are obtained, but the model in the searched flapping-of-wings flight is unstable. This research, then, studies how the flexibly torsional wings effect on the flight stability. Numerical simulations demonstrate that the flexible torsion reduces the flight instability. Moreover, this study develops a precise flexibility model to discuss the effect based on the actual deformation induced by aerodynamic force.