Vibration Analysis of Thick Rotating Cylindrical Shells Based on the Two-Dimensional Elasticity Theory

Abstract

Vibration analysis of infinite thick rotating cylindrical shells is described on the basis of the two-dimensional elasticity theory. Starting from the state of plane strain, the basic equation in the steady rotating state, which is used to obtain the initial stresses, is derived from Hamilton's principle, and the frequency equation, including the effect of the initial stresses due to the rotation, is formulated by Ritz's method. The numerical results for the frequencies in the non-rotating stare are compared with those based on Timoshenko-type shell theory and the available range in the latter theory is examined in terms of the thickness and rotating speed of a shell.