Vibration analysis of a thin eccentric rotating circular cylindrical shell

In this study, the vibration characteristics of a thin eccentric rotating circular cylindrical shell with simply supported boundary conditions are studied. Energy formulations based on Flugge's thin shell theory, Hamilton's principle, and the method of linear approximation are applied to derive the governing equations of motion. In addition to the effects of centrifugal and Coriolis forces, the effect of nonuniform initial stresses resulting from eccentric rotation are taken into account. The natural frequencies of the shell with respect to rotating speed and eccentricity are obtained using Galerkin's method. To validate the present analysis, comparisons are carried out with the results in published literatures and finite element analysis, and good agreements are obtained. The effect of the eccentricity on the natural frequency of the eccentric rotating cylindrical shell is investigated. Some further numerical results are given to illustrate the irregular frequency mutation behaviors resulting from the eccentricity. The effects of the eccentricity on the critical speed and flutter speed of the eccentric rotating circular cylindrical shell are also investigated.