From Fluttering Wings to Flapping Flight: The Energy Connection

Abstract

A new paradigm is presented for understanding flutter and flapping flight. The framework for the investigation is based on conservation of energy. Energy produced, energy lost and/or work done due to structural vibration, aerodynamic wake, and propulsion are taken into account. It is shown that there exist three types of modes in an aeroelastic system, namely 1) unstable mode producing drag (flutter mode), 2) stable mode producing drag, and 3) stable mode producing thrust (flapping flight mode). The type of mode can be determined from the mode shape for a given reduced frequency. The regions (in the modal vector space) corresponding to the three types of modes are presented for a two-dimensional airfoil. It is shown that the flutter region is separate from the thrust-producing region and the boundaries of these regions are tangential to one another at a common neutral point. The neutral point corresponds to no energy transfer between the energy sources. The efficiency of flapping flight and occurrence of flutter is further investigated. Finally, the possibility of a limit-cycle oscillations due to constant thrust flight is presented.