Absolute frequency analysis of traveling waves in a thin-wall laminated composite cylindrical shell rotating on two-ending elastic supports

In this paper, some methods to determine the absolute frequencies of traveling waves in a rotating cross-ply laminated cylindrical shell with elastic supports are investigated. Based on the Sanders' shell theory and by taking into account the Hamilton principle, the governing equations of motion are derived in the rotating coordinate system, which considers the effects of initial hoop tension, the centrifugal and the Coriolis forces due to the rotation as well. The constraint equations of elastic supports are modelled by using artificial distributed elastic springs in the possible directions. By substitution of mode shape profile functions into equations and using the differential quadrature method, the eigenvalue equations of the rotaing shell are derived in both rotating and fixed systems. To make more comparison, the eigenvalue equation of synchronous critical speeds is also derived. Convergence and comparison of the proposed method is investigated through comparing its results with available literature. The comparison results shows that the direction of the corresponding traveling waves and the graphical determination of critical speeds are determined by a more convenient criteria with easier physical interpretation in the fixed system, specially by using the direct method which is more efficient in computation than the converting method.