Dynamics of the dragonfly wings raised by blood circulation

We investigate how the blood flow in the veins in the flapping wings of a dragonfly affects their dynamic response. An idealized model of an elastic tube conveying fluid and rotating around a fixed axis is adopted in this study, based on which governing partial differential equations of motion are obtained by invoking the extended Hamilton's principle. Separation of variables techniques and assumed modes method are employed to solve the resulting equations, and the stabilization analysis is performed to assess the stability of the system. In particular, the coupling effects of tube rotation, deformation, and the movement of the fluid inside are evaluated under different flow rates and rotation speeds. This demonstrates that if the blood in the dragonfly wings flows from humeral angle distally to the wing apex, a stabilization effect can be obtained, and the higher the blood flow rate is, the faster the system will be stabilized. Contrary cases are also studied for further validation of the model.