Influence of embedded material at edges on natural frequencies of rotating annular disk

An analytical method is investigated for the determination of the effect of attaching different materials at one of the edges of annular disk on its natural frequencies. The linear in-plane free vibration of a compound disk in based of two-dimensional plane stress theory is studied to satisfy the displacement and stresses of the disk. The materials used in the disk are considered to be homogenous, elastic and isotropic and the disk is rotating at constant angular speed. In this investigation, the annular disk is considered to be clamped at the inner side and free at the outer edge. The dimensionless natural frequencies for different modes, rotating speeds, and thickness ratios at the inner and outer side are computed.