Dynamic stability analysis of a thin-walled beam subjected to a time periodic gradient bending moment

Abstract

This paper analyzes the dynamic stability of a thin walled beam subjected to non-uniform bending moment. It provides the detail of study the influence of bending moment gradient on instability regions. The second order rotation effect is considered for performing a correct flexural-torsional analysis. The analysis is based on the potential energy principle and adopting the Ritz method. Matrix form of Mathieu-Hill type equation is governed to analyze the stability problem. The paper presents Bolotin's approximations on periodic excitation leads to the stability regions of the structure. Relevant graphs are presented for different loading parameters. Ritz method's terms number and bending moment gradient's coefficient are discussed in detail as well.