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Dynamics and stability of non-linear free vibration of thin rotating rings

Authors
Journal
International Journal of Non-Linear Mechanics
0020-7462
Publisher
Elsevier
Publication Date
Volume
29
Issue
1
Identifiers
DOI: 10.1016/0020-7462(94)90050-7
Disciplines
  • Mathematics

Abstract

Abstract Global dynamics of free non-linear vibration of thin rotating rings are investigated. The rings are circular and exhibit in-plane motions, involving two bending modes with the same circumferential wave number. First, a set of weakly non-linear equations of motion is derived by employing an energy principle. Then the emphasis is placed on obtaining averaged equations for the amplitudes and phases of the modes examined. For a rapidly rotating ring the resulting equations do not involve internal resonance. However, as the spin speed is decreased to small values, the case of the slowly rotating ring is approached, involving 1:1 internal resonance. Finally, the vibration of the stationary ring is obtained as a limiting case of the slowly rotating ring. Based on these sets of averaged equations, the possible types of solutions are first determined and their geometrical and physical interpretation is provided. Then the focus is shifted towards investigating the interrelation and transition between the motions of the stationary, the slowly rotating and the rapidly rotating ring. A complete picture of the dynamics is provided, including stability considerations and effects from internal and external damping.

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