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Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor bladesThe equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades.
Document ID
Document Type
Other - NASA Technical Note (TN)
Hodges, D. H.
(NASA Ames Research Center Moffett Field, CA, United States)
Dowell, E. H.
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
September 3, 2013
Publication Date
December 1, 1974
Subject Category
Structural Mechanics
Report/Patent Number
Accession Number
Distribution Limits
Work of the US Gov. Public Use Permitted.
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