Excitation of Rotationally Periodic Structures

[+] Author and Article Information
S. J. Wildheim

STAL-LAVAL Turbin AB, Department Lb, S-612 20 Finspong, Sweden

J. Appl. Mech 46(4), 878-882 (Dec 01, 1979) (5 pages) doi:10.1115/1.3424671 History: Received December 01, 1978; Revised March 01, 1979; Online July 12, 2010


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,[[ellipsis]] 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.

Copyright © 1979 by ASME
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