中文摘要：

研究了旋转柔性圆盘与周围气膜之间的耦合振动问题。首先给出了基于润滑理论考虑了柔性圆盘振动影响的气膜压力分布的Reynolds方程，以及考虑了盘的旋转离心力、弯曲刚度和气膜压力影响的旋转柔性圆盘的运动方程，然后用有限元对气膜压力方程及旋转柔性圆盘的运动方程进行了离散化，用数值方法求解了旋转柔性圆盘运动与气膜压力的耦合方程，研究了旋转柔性圆盘的气-固耦合振动特性，讨论了周向静载荷的大小、载荷施加位置和气膜厚度对旋转柔性圆盘振动响应的影响。结果表明，周向静载荷的位置对旋转柔性圆盘的振动有很大的影响。一般情况下，周向静载荷越靠近盘的外缘，柔性盘的振动就越大；气膜越厚，柔性盘的振动越大。

英文摘要：

The coupled vibration of a spinning flexible annular circular disk with air film is studied theoretically in this paper. The Reynolds equation of the air film hydrodynamic lubrication with the effect of the disk vibration, and the equation of the spinning flexible annular circular disk with the effect of centrifugal force, bending stiffness, and air film pressure were first presented. Then the Reynolds equation of the air film and the partial differential motion equation of the disk were discretized by using the finite element method. The coupled fields between the air film pressure and the disk vibration displacement were solved by using numerical methods. The effects of circumferential static load and its position, as well as the air film thickness on the disk vibration displacement were dealt with. It is shown that the load position has a great effect on the disk vibration displacements. The disk vibration displacement becomes larger as the load position closes to outer edge of the disk and the air film thickness increases.