English

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

Soft Condensed Matter 2020-03-18 v1

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 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.

Keywords

Cite

@article{arxiv.2003.07763,
  title  = {Synchronous whirling of spinning homogeneous elastic cylinders: linear and weakly non-linear analyses},
  author = {S. Mora},
  journal= {arXiv preprint arXiv:2003.07763},
  year   = {2020}
}