Investigations on the buckling and dynamics of diving-inspired systems when entering water

Abstract

This work provides comparative modeling approaches to determine the velocities and natural frequencies of plunge-diving bird and bioinspired drone systems when entering water. These systems are chosen to further explain the survival of diving birds as they impact water and to provide insight into the design geometry and material choice of bioinspired diving drones. A nonlinear reduced-order model is developed and utilized to analyze the dive at impact considering both Timoshenko and Euler–Bernoulli beam theories. Using Hamilton’s principle, the equations of motion are first derived. Then, static and dynamic buckling analyses are conducted. For this study, a geometrically simplified cone-beam system is considered, where the cone represents the head and the beam represents both the neck and body of the plunge-diving systems. The first study is to analyze the effects different diving drone materials and cone dimensions play on the sensitivity of the system. The second study applies geometric parameters to the cone-beam system representative of a plunge-diving bird (Northern gannet) and a surface-diving bird (Double-crested cormorant). The results show that choosing a material with a higher Young’s modulus and a cone with a smaller half angle increase the velocity at which buckling occurs. The buckling velocities of the predicted Northern gannet model appear to be much greater than the average recorded diving speeds, suggesting that the bird is capable of plunge-diving at more extreme conditions. The natural frequencies are found for the aforementioned plunge-diving systems to predict failure if any external frequencies are known to act on the system while on a mission, such as conditions dependent on the climate or environment. It is shown in all buckling studies that the Euler-Bernoulli beam theory consistently overestimates the responses when compared with the Timoshenko beam theory. In the dynamic responses, Euler–Bernoulli beam theory overestimates for the pre-buckling region, then underestimates at the start of the post-buckling region until a point where the two theories cross paths. The amount of error with Euler–Bernoulli beam theory depends heavily on the slenderness ratio of the beam due to the theory being a simplification of the Timoshenko beam theory. It is noted that as the development of a more realistic bird model improves, the thickness will become significant and the use of Euler–Bernoulli beam theory at the point of impact will no longer be a valid assumption.