Dynamic Modeling of an Insect Wing Subject to Three-Dimensional Rotation

• Published in: International Journal of Micro Air Vehicles Vol. 6; no. 4; pp. 231 - 251
• Main Authors: Jankauski, Mark, Shen, I.Y.
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.12.2014; Sage Publications Ltd
• Subjects: Centrifugal force; Coriolis force; Damping; Discretization; Dynamic models; Elastic deformation; Equations of motion; Euler-Lagrange equation; Finite element method; Flapping wings; Formability; Initial conditions; Insects; Mathematical analysis; Modal response; Numerical integration; Potential energy; Resonant frequencies; Rotation; Three dimensional; Three dimensional models; Vibration mode; Yaw
• ISSN: 1756-8293; 1756-8307
• DOI: 10.1260/1756-8293.6.4.231

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.