Abstract
Stationary whirling of slender and homogeneous (continuous) elastic shafts rotating around their axis, with pin–pin boundary condition at the ends, is revisited by considering the complete deformations in the cross section of the shaft. The stability against a synchronous sinusoidal disturbance of any wavelength is investigated and the analytic expression of the buckling amplitude is derived in the weakly nonlinear regime by considering both geometric and material (hyper-elastic) nonlinearities. The bifurcation is supercritical in the long wavelength domain for any elastic constitutive law, and subcritical in the short wavelength limit for a limited range of nonlinear material parameters.
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