Dynamic instability of truncated conical shells, with variable modulus of elasticity, under periodic compressive forces

Abstract

The dynamic instability of truncated conical shells with variable modulus of elasticity, subjected to periodic axial compressive forces is studied. The formulation of the problem is based on the dynamic version of Donnell type basic equations with bending deformations neglected before instability. By applying Galerkin's method, the basic equations are reduced to a system of coupled Mathieu-Hill equations, from which the principal instability regions are determined by using Bolotin's method. The free vibration problem as well as the classical buckling problem of the shell considered are also discussed.