Vibration Analysis of Free-Free Multi Step Timoshenko Beam under Follower Force Effect with Joint Springs and Concentrated and Distributed Mass Effects

This paper presents the variation in dynamic and static instability characteristics of free-free Timoshenko beam subjected to follower force, where each step has a point mass with transverse and rotary inertia. A finite element code is developed to model two-dimensional Timoshenko beams using the extended Hamilton's principle. The effects of each section length and distributed and concentrated mass on the type of the instability and the critical follower force have been studied for different models of beams. It is concluded that when mass of last section is subsided, the magnitude and the type of instability changes significantly and in most cases it decrease. It is observed that change in rotary inertia parameter of Timoshenko beam and the rotary inertia of concentrated masses affect the magnitude and the type of instability. In this case, by change concentrated mass location, the critical follower force increase suddenly. Effect of joint springs for two section beam with damping and stiffness variation is analysed. Increase in joints parameters lead to more stability.