Helicopter Rotor Blade Flapping and Bending

Abstract

VARIOUS techniques have been described for calculating the stresses in rotor blades, but the early methods suffered from the disadvantage that the aerodynamic forces produced by the deformation of the blade were neglected. This assumption is legitimate only if the possibility of resonance with one or more of the blade bending modes can be ruled out, and it is now known that this is not the case. Measurements of blade stresses at the Cornell Aeronautical Laboratory and at the Massachusetts Institute of Technology have revealed that at certain rotational speeds the higher harmonic stresses may exceed the steady and first harmonic stresses. Unfortunately, the aerodynamic theory is not yet sufficiently developed to predict this result, but even if it were, the actual calculation presents considerable difficulties. The equation of bending is a fourth order partial differential equation with variable coefficients, which has so far defied exact solution, even in the simplest cases. The two independent variables are time, and the spanwise co‐ordinate, but if it is assumed that the aerodynamic loading is produced entirely by the flapping motion of the blade, it is possible to separate the variables, and the problem is reduced to that of solving a fourth order total differential equation, involving only the spanwise co‐ordinate.