Abstract: Focusing on the friction block-brake disc system，local constraint on mobile-simplified coupled system dynamics annular beam structure. Numerical procedure is adopted using the order reduction method，the augment by non-smooth basis function with linear spring，applied to express the local effect. Then the PDE of the disc is reduced to a group of ODEs，in order to get the mode function and the time-varying responses. It is found that the moving modes exist to be the nature of moving load problems. The prominent part and discontinuity（jump）appear in the mode and shear force functions respectively at the position of the moving force.