Rotor Blade Flapping Motion: Simple Model

It has been clearly brought out in Chapter 3 that, during forward flight, the hub loads are dependent on the blade pitch input and the flap response of the blade. The mean hub load expressions have been derived by assuming that the flap response can be represented by a first harmonic variation. Therefore, to complete the solution, one must evaluate the flap response of the blade to a given blade pitch input. The input quantities are collective, lateral, and longitudinal cyclic pitch inputs (θ0, θ1c, θ1s), and the output is the flap response of the blade (i.e., harmonics of the flap response β0, β1c, β1s). These response quantities depend on the configuration of the blade model. Initially, a simplified model will be used to highlight the essential features of the problem; later, additional features will be included in the idealized blade model. In the simplified case, the rotor blade is idealized as a rigid beam hinged at the center of the hub, as shown in Figure 4.1. The rotor blade is assumed to undergo only flap motion.