A rotationally periodic structure consists of a finite number of identical substructures forming a closed ring. The vibrational behavior of such structures is considered, especially the forced response due to a rotating force. It is known that for a rotationally symmetric structure, excited by a rotating force, resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is ωn = nΩ, where Ω is the angular velocity of the force. This resonance condition also holds for a rotationally periodic structure. But then additional resonance possibilities exist, given by ωn = (kN ± n)Ω, where N is the number of substructures and k = 0, 1, 2,… These resonance conditions give a zigzag line in the nodal diameters versus frequency diagram, which here is introduced as the ZZENF diagram. The deformation patterns at the resonances are both forward and backward traveling waves.

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