Considerations for increasing the survivability of Gannet-inspired drones during diving. (15th October 2021) - Zimmerman, S.; Abdelkefi, A.
Abstract: Many external sources of excitation can interfere with the performance of drones, such as propeller or flapping motion. This work investigates the effects external excitation plays on the nonlinear system's dynamics of Gannet-inspired drones. Using Euler-Bernoulli beam theory, the partial differential equations of motion are solved following the Hamilton's principle. Galerkin discretization is then applied to convert the equations of motion to ordinary differential equations in which to obtain an approximation for the nonlinear dynamic response before buckling occurs. The model is inspired by the Gannet bird, where the head is simplified to a cone shape, the neck is resembled by a soft beam, and the rest of the body is represented by a stiff, thicker beam to suggest a buckling behavior physical for the diving bird if buckling is to occur. The results observe the direct effects the external forcing, the damping, the impact velocity, and the boundary conditions have on the resonant frequency range and deflection. The results estimate that increasing the forcing amplitude will in turn amplify the hardening behavior and the maximum displacement. To maintain a lower forcing amplitude consistent with a reasonable external acceleration, a smaller drone mass should be employed. It is observed that higher damping should be applied to minimize the drone's nonlinear effects. The speed at which the drone impacts the water should be chosen to be lower than the estimated buckling speed to avoid lower natural frequencies and to reduce the hysteresis region in order to minimize the nonlinear behavior. From the boundary conditions explored, stiffer boundary conditions should be employed to increase the buckling speed and reduce the deflection when entering water. Highlights: Effects of external excitation on the nonlinear system's dynamics of Gannet-inspired drones are investigated. Galerkin discretization is applied to convert the equations of motion to ordinary differential equations. Increasing the forcing amplitude amplifies the hardening behavior and the maximum displacement. It is observed that higher damping should be applied to minimize the drone's nonlinear effects. Stiffer boundary conditions should be employed to increase the buckling speed and reduce the deflection.