The steady-state response of a rotating ring subjected to a stationary load

Abstract

The in-plane steady-state response of a rotating ring on elastic foundation subjected to a stationary load is investigated theoretically using a high-order model in the framework of the plane strain assumption. The adopted high-order model accounts for the through-thickness variation of stresses and displacements, as well as the boundary tractions at the inner and outer surfaces of the ring. Based on the ratio of the foundation stiffness to the stiffness of the ring, two configurations of the ring-on-foundation system are investigated, namely soft foundation (stiff ring) and stiff foundation (soft ring). The analytical “method of the images” is used to obtain the ring response. It is found that the response of a stiff ring to a stationary load of constant magnitude is governed by the translational rigid body-like motion. In contrast, in the case of a soft ring, a wave-like deformation is predicted for the rotational speeds higher than a critical one. It is for the first time that such wave-like displacements are predicted using a rotating ring model with the rotation effects being properly considered. The response of a rotating ring to a stationary harmonic load is studied too. The predicted displacements using the high-order model are compared with those obtained from the classical low-order model in which only the radial and circumferential displacements at the middle surface of the ring are considered. It is concluded that only in the case of a stiff ring, the classical low-order model and the high-order model give similar predictions. When the ring is soft, the predictions of the two models deviate significantly. Resonances of a stationary ring under a moving load and a rotating ring subjected to a stationary load are compared in terms of the resonance speeds and the steady-state responses. It is shown that these two situations can not be treated as equal in many cases.