中文摘要：

针对汽轮机自带冠叶片的接触减振机理问题，考虑惯性力和气流激振力对叶片振动的影响，采用Hertz接触力模型和悬臂梁振动理论建立了自带冠叶片接触碰撞的动力学模型。利用Galerkin模态截断方法，截取系统第一阶模态，实现对悬臂梁系统的降维处理。对降维后的系统，采用谐波平衡法分别获得了系统在有阻尼和无阻尼情况下的解析解。所得结果为自带冠叶片接触碰撞问题的进一步研究提供了理论依据。

英文摘要：

Integrally shrouded blade contact motion model was established by using Hertz contact force model and cantilever beam vibration theory based on integrally shrouded blade contact damping mechanism and considering the effect of the inertial force and the air-exciting-vibration force acting on the blade. The cantilever beam model was discreted by Using Galerkin method, and intercepted the first order mode of a cantilever beam, realized the process of reduced dimension on cantilever beam system. The analytical solutions with and without damping are deduced by Harmonic balance method. The obtained results for integrally shrouded blade contact and collision characteristics research provides a good theoretical basis.