Free Vibration Analysis of Thin Cylindrical Shells by the Differential Quadrature Method

Abstract

By introducing the application of the differential quadrature method (DQM) to the dynamic analysis of thin circular cylindrical shells, the work of this paper makes a step forward in furthering the potential of the DQM in the area of structural mechanics. The problem is identified by an eighth-order system of coupled partial differential equations in terms of the three displacement components. The proposed differential quadrature solution is semi-analytical in that Flu¨gge’s representation of the displacement components by trigonometric sine and cosine functions of the circumferential coordinate is employed. The results of the differential quadrature solutions of the natural frequencies of various shell cases are compared and shown to be in excellent agreement with the published, and also some recalculated, results of exact solutions for freely supported, clamped-clamped, clamped-free, and free-free shells. Comparisons are also made with the published experimental data of clamped-clamped and clamped-free shells.