Non-conservative stability of spinning pretwisted cantilever beams

•Investigating the effect of follower forces on the stability of the spinning pretwisted cantilevers.•Considering the effect of viscoelastic medium on the stability of the system.•Providing useful figures for designing the spinning pretwisted beams.

The stability of a pretwisted cantilever beam spinning about its longitudinal axis and subjected to non-conservative force is investigated. In this study, it is assumed that the cantilever is embedded in viscoelastic medium, which is modeled by the Kelvin-Voigt foundation. Two different types of the non-conservative force are considered. The governing equations of motion and boundary conditions are derived by using Hamilton's principle. The finite element method is utilized to transform the coupled equations of motion to a general eigenvalue problem. The proposed model is justified by an excellent agreement between the present results and those reported in the literature. The effects of several design parameters including the pretwist angle, the cross section ratio, the viscoelastic parameters and load span length on the stability of the spinning pretwisted cantilevers are also examined. Moreover, the critical load and spinning speed and stability regions of the spinning cantilevers are identified. The results show that the design parameters significantly change the stability of the spinning pretwisted cantilever beams.