A three-dimensional flutter theory for rotor blades with trailing-edge flaps

Abstract

This dissertation develops the equations of motion for the structural and aerodynamic forces and moments of a rotor blade with a trailing-edge flap using eight degrees of freedom. Lagrange's equation is applied using normal modes to find the flutter frequency and speed similar to the classic fixed-wing method developed by Smilg and Wasserman. However, rotary-wing concerns are addressed including different freestream velocities along the blade (variation of reduced frequency along the span of the rotor blade) and the influence of previously shed vortices on the aerodynamic forces and moments (Loewy's returning wake). While Loewy [Ref. 49] did not explicitly state that his 2-D theory would apply to rotor blades with trailing-edge flaps, the manner in which the theory was developed allows it to be applied in this manner. Comparisons to classic 1DOF, 2DOF and 3DOF flutter theories are made to validate this theory in the limiting cases. Flutter analyses, including g-. plots, of an example rotor blade with five degrees of freedom are performed for various rigid body flap frequencies. Classic methods of rotor blade design of ensuring freedom from flutter are to collocate the center of gravity (c.g.), elastic axis (e.a.), and aerodynamic center (a.c) at the 25% chord. With the development of rotor blades with trailing-edge flaps, it is shown that this current design practice is not valid when a trailing-edge flap is incorporated.