The Stressing of Rotor Blades: A Simplified Approach to a Complicated Problem in Applied Mathematics

NUMEROUS difficulties are encountered in any attempt to ascertain the loads which come into action on a gyroplane rotor blade, and the stresses which these loads impose on the blade. The loads are not steady but variable, complicated and subject to intractable fluctuations. In consequence the blades are in a continual state of agitation. Even when various simplifying assumptions are made the resulting differential equations of motion do not readily yield to conventional methods of treatment. So far as the modes of free vibration are concerned the analysis is relatively simple, but so far as the stresses in forced vibration are concerned the difficulties are formidable. In this paper it will be assumed that the loading over the blade is steady at any instant of a given flight condition. Subject to this restriction, the stresses in the blade may be found to any required degree of approximation by the generalised theorem of three moments suitably modified. In addition the gyroscopic moments of a blade and its frequency of “Happing” vibration will be found on the assumption that the blade is rigid and regard being had to imposed rotation.