Analyses of rigid-flexible coupling dynamic properties of a rotating internal cantilever beam

Abstract

The rigid-flexible coupling dynamic properties of an internal cantilever beam attached to a rotating hub are studied in this paper. Based on the accurate description of non-linear deformation of the flexible beam, the first-order approximation coupling model is derived from Hamilton theory and assumed mode method, taking into account the second-order coupling quantity of axial displacement caused by transverse displacement of the beam. The simplified first-order approximation coupling model which neglects the effect of axial deformation of a beam is presented. The simplified model is transformed into dimensionless form in which dimensionless parameters are identified. Firstly, the dynamic response of an internal cantilever beam is compared with that of an external cantilever beam, which are both in non-inertia system. Then, the stability of an internal cantilever beam is analyzed. Finally, the convergence of critical rotating speed of an internal cantilever beam is analyzed. Generally, it is pointed that an internal cantilever beam has a dynamic softening phenomenon, which is different from the dynamic stiffening phenomenon of an external cantilever beam. The critical ratio of the internal radius to the length of the beam for unconditional stability and the critical rotating speed of conditional stability of an internal cantilever beam are derived. When the first natural frequency decreases as the rotating speed increases, the dynamic system of the internal cantilever beam is conditionally stable. As the number of modes increases, the critical rotating speed of an internal cantilever beam decreases, and it has a convergent value.