A NEW METHOD FOR IN-PLANE VIBRATION ANALYSIS OF CIRCULAR RINGS WITH WIDELY DISTRIBUTED DEVIATION

A new analytical method was developed to predict the in-plane mode shapes and the natural frequencies of a ring with widely distributed deviation. The Laplace transform was used to find the exact solution of eigenvalue problem without assuming any trial functions and finite elements. The widely distributed deviation was effectively formulated in the theory using Gauss–Legendre quadrature. The validity of the proposed method was examined through finite element analysis and modal test. The effects of partial change of the density, the stiffness, and the thickness on the natural frequencies of the ring were investigated.