Study of the optimal natural frequency ratio of a hawkmoth-like flapping wing

This paper presents a study of the optimal frequency ratio of a hawkmoth-like wing, defined as the ratio between the first natural frequency of the wing structure and the flapping frequency in terms of energy and force production. A fluid-structure interaction framework based on multibody dynamics and an unsteady vortex lattice was employed. The results show that when the natural frequency ratio is approximately 2.0, the aerodynamic force and power efficiency are maximized. At the same frequency ratio, wings with softer tip structures tend to be more efficient. These findings can provide some insights into the mechanism of natural selection for insect wing structures, which can be applied to the design process of flapping-wing micro air vehicles. © 2025 Elsevier Masson SAS