Motion of an unarticulated helicopter blade with application to the problem of vibration of the rigid rotor helicopter

The present investigation concerns itself almost completely with the derivation and solution of the equations of motion of the helicopter blade. The fluctuating aerodynamic forces which cause flapping in the hinged rotor bend the blades of the rigid rotor in a vertical plane. The effect of the bending is to cause fluctuating moments on the rotor hub. This pure bending oscillation is the most obvious cause of vibration and is treated here. Coupled motions are not considered and are effectively eliminated by the assumption that the mass center, aerodynamic center and elastic axis are at the point on each cross section of the blade and that the elastic axis is a straight line. Although this work was undertaken to investigate rotor vibration, it has broader significance. It is, in effect, the essential step which makes possible the rational analysis of all rigid rotor dynamics and aerodynamics. It is directly comparable in importance to the solution of the problem of the blade flapping motion in hinged rotor work. For example, once the bending of the blade in forward flight is known such information as 1. Fatigue stresses in the blades 2. Control lag angle required 3. Maximum deflection of the blades, etc. is immediately available