介绍一种求解Laplace方程边值问题的半解析方法，该方法的基本思想是交替运用边界条件的不同部分，迭代求出满足实际边界条件下的解。它具有计算简便和保留解的级数形式等优点。给出利用这种方法求解工程中实际问题的几个例子，包括混合边界条件问题、圆缺域、多连域和圆柱内存在球型空穴等问题。数值计算结果说明，对于以上问题及相关情况的求解是有效的。

The vibration of a rotor rubbing a staler caused by an initial perturbation was studied analytically. The analytical model consists of a simple disc shaft rotor and a fixed slator. The perturbation is an instantaneous change of the radial velocity when the rotor is operating in its normal steady state. The analysis showed that the rotor may continue rubbing the stator for small clearance, even if the initial perturbation no longer exists. For the interest of engineering applications, we investigated various rotating speeds, perturbalion amplitudes and clearances between the rotor and the stator, Various friction coefficients on the contact surface were also considered. The graphical results can be used for the design of rotating machines.

This paper discusses the vibration phenomena of a rotor rubbing with a stator caused by an initial perturbation. The analytical model consists of a simple disc-shaft rotor and a fixed stator. The perturbation is an instantaneous change of the radial velocity when the rotor is rotating in its normal steady state. It is found that under certain conditions, the rotor will remain rubbing with the stator, even if the initial perturbation no longer exists. In the case of no friction on the contact surface between the rotor and the stator, the full rubbing behaves as forward whirling. When friction is present, the full rubbing behaves as backward whirling.