Modal analysis of contact system is complex due to its non-linear and chaotic behaviors in the process.This paper builds up the equivalent linear model of labyrinth air seals with damping-ring/sleeves by introducing local contact stiffness and using vibration mechanic theory.The experimental results of natural frequencies and mode shapes of the labyrinth air seals with damping-ring/sleeves verified the validity of the proposed simplified model and the simulation results by finite element method(FEM).The influence of variable parameters(position

width

thickness and gap size)of damping-ring/sleeves are also studied.