Enhanced design considerations on the buckling and dynamics of Gannet-inspired systems during water entry

To provide a more complete analysis of Gannet birds and Gannet-inspired drones during diving, this work considers an improved beam model to describe the static and dynamic characteristics of Gannet and Gannet-like drones at impact. The beam model consists of two different geometric and material property beams under continuity conditions to better understand the geometrical and material parameters' influence on the structural statics and dynamics of these kinds of systems. Using Hamilton's principle, the equations of motion, continuity, and boundary conditions considering Euler-Bernoulli and Timoshenko theories are derived. Then, applying the continuity and boundary conditions, the static and dynamic analyses are conducted to examine the impact buckling speeds, the buckled shapes, the natural frequencies at different impact velocities for bioinspired drone design, and the post-buckled mode shapes. The buckled configurations suggest that the body of the Gannet most likely has a different bending and torsional stiffness than the neck. The results indicate that the amount of softening in the joints contributes significantly to not only the speed at which the bird will buckle, but also the buckling profile of the bird. To obtain a physical buckling profile of the Gannet, a stiffer boundary condition at the end of the bird body model is needed due to the increased bending stiffness properties of the body compared to the neck as well as the position of the wings and feet surpassing the end of the body. The results also demonstrate that to build a bioinspired diving drone that falls within a smaller air-vehicle range, the amount of error between theories in predicting the static and dynamic buckling behavior of the system becomes significantly more evident. The dynamic characteristics and mode shapes of the Gannet-like systems are provided for further drone design insight on the impact speeds the drone can achieve without responding to an external excitation frequency from a propeller or actuator.