The differential equations of motion for the rotor blade are derived in this chapter. First the focus is on the inertial and structural forces on the blade, with the aerodynamics represented by the net forces and moments on the blade section. Then the aerodynamic loads are analyzed in more detail to complete the equations. In subsequent chapters the equations are solved for a number of fundamental rotor problems, including flap response, aeroelastic stability, and aircraft flight dynamics. In Chapter 6 the flap and lag dynamics of an articulated rotor were analyzed for only the rigid motion of the blade, including hinge spring or offset. The present chapter extends the derivation of the equations of motion to include a hingeless rotor, higher blade bending modes, blade torsion, and pitch motion. The corresponding hub reactions and blade loads are derived, and the rotor shaft motion is included in the analysis.
The rotor blade equations of motion are derived using the Newtonian approach, with a normal mode representation of the blade motion. The chapter begins with a discussion of the other approaches by which the dynamics can be analyzed. Engineering beam theory is commonly used in helicopter blade analyses. The blade section is assumed to be rigid, so its motion is represented by the bending and rotation of a slender beam. This is normally a good model for the rotor blade, although a more detailed structural analysis is required to obtain the effective beam parameters for some portions of the blade, such as flexbeams and at the root.