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

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.

Harnessing Gravity‐Induced Instability of Soft Materials: Mechanics and Application

“…When subjected to centrifugal forces, these soft solids can undergo deformation and buckling instability. [ 95–100 ] In the case of a disk, it has been observed that the deformation and buckling are most pronounced near its inner edge ( Figure a). Studies shown that increasing the rotating speed not only shifts the buckling deformation toward the inner edge of the disk but also increases the wavenumber of the buckling.…”

“…On the other hand, for a solid cylinder, increasing the rotating speed does not alter the buckling mode but results in an increase in the buckling amplitudes (Figure 7b). [ 98 ] This suggests that higher rotational speeds primarily affect the magnitude of the buckling deformation in the cylinder while maintaining the same mode of buckling. The understanding of the mechanical behavior of rotating soft solids is crucial in various applications.…”

“…b) The buckling amplitudes of solid cylinder with the increase of rotating speed (left to right). Reproduced with permission [98]. Copyright 2020, Springer Nature.…”