Nonlinear deformations of a slender rod rotated at one end
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A thin elastic rod is rotated at one end. The nonlinear deformations due to centrifugal forces are studied. The problem is governed by a nondimensional parameterJ which signifies the relative importance of rotation to flexibility, and the angle a between the rotation axis and the clamped end. The nonlinear differential equations are solved by three different perturbations and also numerical integration for the rangeJ≤5. Force, moment and displacement characteristics are determined. The solutions are unique for smallJ. Three solutions are possible, one may be unstable, for largerJ. Catastrophic changes may occur whenJ is decreased.
KeywordsDifferential Equation Mathematical Method Rotation Axis Centrifugal Force Nonlinear Differential Equation
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