Nonlinear vibration and dynamic instability of thin shallow conical shell

摘要

Based on the dynamic version of Marguerre's equations, the nonlinear vibration and dynamic instability of thin shallow conical shells subjected to periodic transverse and in-plane loads are studied under two different boundary conditions. Applying Galerkin's method, the basic equations are reduced to a system of Duffing and Mathieu equations, from which various kinds of nonlinear vibration and dynamic instability are determined using numerical methods. For illustration, nonlinear vibration frequencies and dynamic instability regions for a particular conical shell are determined. The effects of static load as well as static snap-buckling on the instability regions are also examined.