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This paper presents a two‐dimensional corotational curved beam element for the dynamic analysis of curved viscoelastic beams with large deformations and rotations. In contrast with traditional straight beam elements, the novelty of the presented formulation lies in introducing a curved reference configuration, which follows the rotation and translation of a corotational frame, to measure the pure elastic deformation of the beam and describe the spatial position of an arbitrary material point. A curvilinear coordinate system is fixed on this reference configuration to measure the local deformation of the element. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. An accurate two‐node curved element and the Kelvin–Voigt model are introduced to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational accuracy, and computational efficiency of the presented formulation. Moreover, the effects of the internal damping and external damping on the dynamic response of a rotating curved beam are investigated. [ABSTRACT FROM AUTHOR]