A Consistent and Systematic Approach for Modeling Radially Rotating Flexible Beams

Many formulations are presented in the literature to simulate the dynamic behavior of radially rotating flexible structures. Their drawbacks stem from predicting an unstable response for a physically stable system or from inconsistently considering the geometric nonlinearities of the system. In this study, the equations of motion for a radially rotating flexible beam are derived by considering the geometric nonlinearity in the von Kàrmàn sense, the axial geometric shortening of the beam and the stiffening effect induced by the centrifugal force. The current formulation is assessed by comparing its results to those predicted by five other methodologies that are reported in the literature. Both static and dynamic analyses were performed. The results demonstrate the instability predicted by the “conventional” method, the stiffening effect of the centrifugal force, the overestimation of the beam stiffness through the inconsistent consideration of the geometric nonlinearity in the von Kàrmàn sense, the deficiencies of the “consistent linearization” technique and the stabilizing characteristic of the axial geometric shortening effect.