The dynamic behaviour of cylindrical shells reinforced by ring ribs—II. Shells of finite length

Abstract

A circular cylindrical shell reinforced by ribs of limited rigidity and equidistant from each other, clamped by the edges, is under the action of an impulsive load. The basic assumptions are identical to those of part I [1].When the ribs are placed rather frequently the solution to the problem is obtained from those obtained in part I [1] by a change of notation, so we consider below that the ribs are placed “sparsely”. The cases of “small”, “medium” and “large” loads are investigated; the differential equations of motion are listed in a form suitable for numerical integration by an electronic computer for every case. As the distance of the spans from the shell's edges varies the dynamical behaviour of the spans is generally different. It is shown by numerical calculation of some concrete examples that cetera paribus with sufficient accuracy we may consider the dynamic behaviour of all spans, except extreme ones, identical to that of an infinitely long shell, and the extreme spans moment can be analysed by means of the example of a shell clamped by the edges with one ring in the middle. For the values of the parameter μ satisfying μ ≥ μ1 ≤ √6 this is confirmed analytically.