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.

中文翻译：

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旋转环在固定载荷作用下的稳态响应

摘要 在平面应变假设的框架内，利用高阶模型，从理论上研究了弹性地基上旋转环在静载荷作用下的平面稳态响应。采用的高阶模型考虑了应力和位移的厚度变化，以及环内外表面的边界牵引力。基于地基刚度与环刚度之比，研究了地基系统的两种配置，即软基础（刚性环）和刚性基础（软环）。解析“图像方法”用于获得环响应。发现刚性环对恒定大小的静止载荷的响应受平移刚体状运动的控制。相比之下，在软环的情况下，对于高于临界转速的旋转速度，预计会出现波浪状变形。这是第一次使用正确考虑旋转效应的旋转环模型来预测这种波状位移。还研究了旋转环对静止谐波载荷的响应。将使用高阶模型的预测位移与仅考虑环中间表面的径向和周向位移的经典低阶模型获得的位移进行比较。得出的结论是，只有在刚性环的情况下，经典的低阶模型和高阶模型才能给出相似的预测。当环是软的时，两个模型的预测有很大的偏差。根据共振速度和稳态响应，比较了在移动负载下的固定环和在固定负载下的旋转环的共振。事实证明，这两种情况在很多情况下是不能平等对待的。