Optimum design of conical shells for free vibration

Abstract

Optimum design of conical shells for free vibration is treated herein by considering the lowest frequency corresponding to an axisymmetric mode. For a given volume of the shell, the inner base radius and the slope of the inner wall are kept constant, whilst the outer wall has piecewise constant slopes with no abrupt changes in thickness. Parameters in the study are the inner base radius to height ratio, number of slopes of the outer wall and the semi-vertex angle of the cone. Results indicate considerable elevation in frequencies for the shells restrained at the base and free at the top. The problem of determining the minimum volume for a prescribed frequency is also treated and the study shows that a reasonable amount of saving in material is possible. A numerical procedure incorporating the complex optimization technique and the finite element method is used. © 1988.