Development of analytical solution for dynamic behavior of elastic flapping wing under inertial loading

Structural dynamics (SD) behavior of an Elastic Flapping Wing (EFW) is analytically investigated for the first time. Due to importance of inertial forces and in order to seek analytical solution for EFW, they are the only forces considered in this study. The EFW governing equations are derived via a modal approach. A second order dynamic servo actuator is utilized to impose a sinusoidal motion on the EFW. The accelerated forcing effect of the servo on EFW is also analytically computed and augmented to the governing equations. The governing equations are next solved in a closed form. The EFW analytical solution allows for various analysis of its steady and transient response due to any changes in the forced motion and/or its structural parameters. Finally, as a case study, the EFW is modeled using elastic beam and shell elements in order to investigate its dynamic behavior while undergoing a prescribed sinusoidal motion. The proposed development paves the way for further analytical studies in the area of EFWs.