Synchronous whirling of spinning homogeneous elastic cylinders: linear and weakly nonlinear analyses

Serge Mora (1)

1 PMMD - Physique et Mécanique des Milieux Divisés

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 wave length is investigated and the analytic expression of the buckling amplitude is derived in the weakly non-linear regime by considering both geometric and material (hyper-elastic) non-linearities. The bifurcation is super-critical in the long wave length domain for any elastic constitutive law, and sub-critical in the short wave length limit for a limited range of non-linear material parameters.

Mots clés: Asymptotic analysis; Elasticity; Bifurcation; Instability

Domaines: Sciences de l'ingénieur [physics]

Serge Mora. Synchronous whirling of spinning homogeneous elastic cylinders: linear and weakly nonlinear analyses. Nonlinear Dynamics, 2020, 100 (3), pp.2089-2101. ⟨10.1007/s11071-020-05639-x⟩. ⟨hal-02733481⟩