Coupled Dynamic Instability Analysis of Thin-Walled Columns Subjected to Harmonic Axial Loading

Abstract

This paper presents triply coupled vibrations and instability analysis of thin-walled columns having a non-symmetrical open cross-section. Vlasov’s theory is used to derive the governing differential equations for coupled flexural and torsional vibrations. A numerical method is presented to determine the exact natural frequencies and corresponding mode shapes in terms of real functions. Employing Galerkin’s method, the coupled partial differential equations are reduced to a set of coupled Mathieu type equations. Following Bolotin’s method, the principal instability regions of thin-walled column with a non-symmetrical cross-section having various boundary conditions are determined. Numerical examples are presented to examine the effect of different boundary conditions, aspect ratios, static and dynamic load factors on principal instability regions. The study of response and corresponding phase plot in stable and unstable regions are carried out to identify the dynamic instability behavior.