Dynamic modeling of an insect wing subject to three-dimensional rotation

Abstract

A dynamic model of an insect wing is developed treating the wing as a deformable body subject to three-dimensional finite rotation about a fixed point at the base of the wing. Discretization of a stationary wing is first conducted via finite element analysis to determine the natural frequencies and mode shapes of the wing. By formulating and discretizing the kinetic and potential energy, we derive the equation of motion governing the modal response of a flapping wing using Lagrange's equation. The equation of motion indicates Coriolis, Euler, and centrifugal forces resulting from the finite rotation are responsible for the wings elastic deformation. Numerical integration reveals a beat phenomenon that arises from the Coriolis excitation in the first vibration mode. The beat phenomenon is insensitive to yaw amplitudes and nonzero initial conditions but diminishes in the presence of damping. The beat phenomenon can potentially be used to estimate gyroscopic forces.