An analytical method is presented for predicting the effects of local deviations such as a point mass, a sharp decrease in stiffness and variation of thickness on the free in-plane bending vibration characteristics of nearly axisymmetric rings. The approach is based on the Laplace transformation method and the expression of local deviation as the variation of heaviside unit step function. The effects of local deviation on the natural frequencies and mode shapes of the rings are predicted for the proposed nondimensional mass and stiffness parameters. The validity of the approach was examined through modal testings and/or finite element computation.

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