An analytical method is developed for the determination of modal vibration characteristics of high speed rotating annular disks. A systematic approach based on established solutions for the linear in-plane free vibrations of the disks which satisfy the displacement and stresses compatibilities is developed. The disk is considered to be a homogeneous, thin and elastic isotropic, and it is rotating at constant angular speed. The developed analytical solution was obtained by implementing the two-dimensional plane stress theory. In this research, fixed-free and free-free boundary conditions for the annular disks are considered, and natural frequencies, as well as mode shapes of the rotating disks, are computed. The mode shapes are represented by eight functions in polar coordinates. The dimensionless natural frequency parameters are depicted for free vibration of the system for a range of dimensionless rotation speed and radius ratios. Also, the results provide several non-dimensional critical speeds.

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