Survey and comparison of engineering beam theories for helicopter rotor blades

Nomenclature A = blade cross-sectional area #!, B2 = blade cross-sectional constants E = Young's modulus e = blade root offset eA = tension axis chordwise offset F = internal forces / = applied forces G = shear modulus H = angular momentum Iv. = area moment of inertia about the deformed y axis /,. = area moment of inertia about the deformed z axis J = polar moment of inertia K = moment strain km = polar radius of gyration kml = blade chordwise radius of gyration km2 = blade flapwise radius of gyration Lv = in-plane load Lw = out-of-plane load M = internal moment My = torsion load m = blade running mass, applied moment, Eq. (16) P — linear momentum q = generalized displacement R = blade length r = blade length coordinate T — tension u = blade extension V = generalized linear speeds v = in-plane blade bending w = out-of-plane blade bending y = force strain 6 = blade twist <p = blade torsion i// = generalized rotation fl = rotor speed, generalized angular speeds, Eq. (16)

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