A geometric softening phenomenon of a rotating cantilever beam

• DOI: 10.1007/s00419-017-1231-3
• Publication Date: 2017-03-02T04:35:54Z
• Authors: Guowei Zhao; Jianming Du; Zhigang Wu
• Keywords: Stiffening

In this study, we reconstructed a dynamic model of a rotating cantilever beam for which the geometric stiffening term was obtained by accounting for the longitudinal shrinkage caused by the transverse deflection of the beam. Previous investigations focused on kinetic energy but neglected strain energy. For this study, we retained these strain energy coupling terms. We used Hamilton’s principle to derive the complete coupling model. Taking the effect of steady-state axial deformation into account, we obtained the transverse equation of motion and the coupling general characteristic equation. Unlike previous models, this model incorporates not only the geometric stiffening effect but also the geometric softening effect. In relevant numerical examples, as the angular velocity increases, the bending frequency gives rise to geometric stiffening in line with the results obtained in previous studies. When the angular velocity reaches and exceeds a critical value, the bending frequency produces a geometric softening phenomenon.