A Theoretical Method for Calculating Flexure and Stresses in Helicopter Rotor Blades: Development of a Variational Procedure based on the Rayleigh‐Ritz Method which Leads to a Rapid Estimation of the Flapwise Vibration Modes and Frequencies

A variational procedure is developed, in the form of an extension of the Rayleigh‐Ritz method, leading to a rapid estimation of the flapwise vibration modes and frequencies of a helicopter rotor blade. The initial data required are the blade mass and stiffness distribution and the angular velocity of the rotor blade. The normal modes and frequencies are subsequently used to determine blade shapes in flight. The aerodynamic forces only enter at a late stage of the analysis, and the effect of differing flight conditions is readily assessed. The method makes extensive use of matrix formulation and particularly lends itself to electronic computation techniques. A numerical example is given for the special case of constant spanwise blade mass distribution, although the method may readily be extended to cover this restriction. The bending moment distribution is also worked out, and flexible and rigid blades are compared.