DYNAMIC CHARACTERISTICS ANALYSIS OF A ROTATING FLEXIBLE CURVED BEAM WITH A CONCENTRATED MASS

The dynamic characteristics of a planar rotating flexible curved beam with a concentrated mass are studied in this paper. The curved beam element is derived based on the absolute nodal coordinate formulation. The element adopts the Green-Lagrangian strain, and the virtual work of the elastic force of the curved beam element is calculated according to the curvature change before and after the deformation of the curved beam and the exact expression of the curvature. Through the virtual work principle, the nonlinear dynamic model of rotating flexible curved beam with a concentrated mass is established by using the \delta function and the fixed boundary condition between the hub and the cantilever curved beam. Based on this model, the pure bending problem of cantilever curved beam and the dynamic response of rotating flexible curved beam with rigid-flexible coupling effect are simulated. According to the results, the convergence of the proposed element and the correctness of the dynamic model are discussed, respectively. Furthermore, applying the D'Alembert principle, the rotating curved beam is equivalent to a non-rotating curved beam with centrifugal forces, and the characteristic equations of the system are obtained by linear perturbation processing. The effects of rotating angular velocity, initial curvature and concentrated mass on the dynamic characteristics of the curved beam are studied, respectively. Finally, the frequency loci veering and mode shift of the rotating curved beam are analyzed, and the interrelation between them is expounded. The results show that with the increase of rotation angular velocity, the frequency characteristics of curved beams are similar to straight beams, and the mode shapes of curved beams dominated by tensile deformation will be advanced.