Excitation of rotating circumferentially periodic structures

Abstract

A circumferentially periodic structure consists of a finite number of identical substructures coupled together in identical ways to form a closed ring-type structure. The vibrational behaviour of such structures when rotating about the axis of structural symmetry is considered, especially the forced response due to forces fixed in space. It is known that for a circumferentially symmetric structure, rotating about its axis of structural symmetry and excited by a force fixed in space, resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is ω n = nΩ , where Ω is the angular velocity of rotation. The deformation at these resonances consists of waves travelling backwards (in relation to the direction of the structure rotation). This resonance condition also holds for a circumferentially periodic structure. But then additional resonance possibilities exist, given by ω n = (kN ± n)Ω , where N is the number of sub-structures and k = 0, 1, 2, …. These results are known to hold true for a structure fixed in space and acted upon by a rotating force. In this paper these results are shown to hold true also for a rotating structure acted upon by a force distribution fixed in space. Both backward and forward travelling waves can be excited. In those cases when the rotating structure exhibits Coriolis accelerations the natural frequencies for backward ( ω 1 n ) and forward ( ω 2 n ) rotating mode shapes are different. This well-known property has a pronounced effect on the forced response due to forces fixed in space. In the absence of Coriolis effects the magnification factor is essentially 1 (ω n 2 − ω 2) , where ω is the forcing frequency due to rotation. But in the presence of Coriolis effects the magnification factor has the characteristics 1 (ω 1n − ω)(ω 2n + ω) .