An efficient three-degree-of-freedom equivalent model for vibration analysis of rotating planar circular-arc beams

To analyze the transient response and vibration characteristics of planar rotating circular-arc beams, this paper proposes an efficient three-degree-of-freedom equivalent dynamic model. Unlike conventional multi-element discretization methods, the proposed model constructs an analytical displacement-field interpolation operator directly from the static closed-form analytical solution of a cantilever circular-arc beam subjected to prescribed free-end displacements and subsequently incorporates this operator into the dynamic formulation of the rotating beam. The continuous deformation of the whole circular-arc beam is then represented by only three generalized coordinates, namely the free-end tangential displacement, radial displacement, and cross-sectional rotation, leading to a low-dimensional yet accurate description of the beam deformation. In the rotating reference frame, the governing equations are derived using Hamilton’s principle. The model accounts for axial deformation, bending deformation, shear deformation, Kelvin-Voigt internal damping, gyroscopic velocity coupling, rotational dynamic softening, and centrifugal prestress stiffening. The validity and accuracy of the proposed model are verified by comparison with finite element results in terms of static displacement fields, transient dynamic responses, and natural frequencies. The results show that the model can accurately capture the dominant low-order vibration characteristics of rotating circular-arc beams while significantly improving computational efficiency. Parametric studies further reveal the effects of rotational speed, initial curvature, and internal damping on the steady-state response and damped natural frequencies. Under high rotational speeds and large curvatures, the centrifugal prestress-stiffening, dynamic-softening, and gyroscopic terms have significant influences on frequency prediction and should be retained in the dynamic modeling of rotating circular-arc beams.