The aeroelastic equations of motion for the rotor were derived in Chapter 16. The present chapter examines the solutions of these equations for a number of fundamental stability problems in rotor dynamics. To obtain analytical solutions, each problem must be restricted to a small number of degrees of freedom and to only the fundamental blade motion. Rotorcraft engineering currently has the capability to routinely calculate the dynamic behavior for much more detailed and complex models of the rotor and airframe. Thus elementary analyses are less necessary for actual numerical solutions, but are even more important as the basis for understanding the rotor dynamics.

Pitch-Flap Flutter

Traditionally, the term “flutter” refers to an aeroelastic instability involving the coupled bending and torsion motion of a wing. For the rotary wing, flutter refers to the pitch-flap motion of the blade. Often the term is generalized to include any aeroelastic instability of the rotor or aircraft, but the subject of this section is the blade pitch-flap stability. The classical problem considers two degrees of freedom: the rigid flap and rigid pitch motion of an articulated rotor blade. Since the control system is usually the softest element in the torsion motion, the rigid pitch degree of freedom is a good representation of the blade dynamics. A general fundamental flap mode with natural frequency υβ is considered. A thorough analysis of the flutter of a hingeless rotor blade usually requires that the in-plane motion be modeled as well.