Instability Characteristics of a Free-Free Multi-Stepped Timoshenko Beam with Concentrated Masses Subjected to Follower Force

This paper presents dynamic and static instability characteristics of a free-free multi-stepped Timoshenko beam subjected to a follower force, where each step has a point mass with transverse and rotary inertia. A finite element code is developed to model two-dimensional multi-stepped Timoshenko beams using the extended Hamilton's principle. The effects of each section parameters on the type of instability and critical follower force have been studied for different models of multi-stepped beams. It is concluded that the assumption of a uniform beam to study most aerospace structures such as launch vehicles could lead to an unrealistic instability analysis, where any small change in the characteristics parameters for each step could change the instability behavior significantly. Furthermore, this paper introduces a new parametric approach concept for analyzing the characteristics effects of a multi-step aerospace structure.