The Effect of Mass and Section Properties on Instability Characteristics of Free-Free 3 Stepped Timoshenko Beam, Subjected to Controlled Follower Force

In this research، a free-free Timoshenko beam was used as a mathematical model to investigate static and dynamic characteristics of a typical type of aerospace structures. For this purpose، stepped Timoshenko beam was modeled، considering the shear deformation and rotary inertia parameters. The external force was combination of a follower force and the control system force in the direction of the force. The conservative and non-conservative parts of the acting force were taken into account in this analysis. Hamilton’s principle was used to develop the governing equations. The whole mathematical model was solved using finite element method. The results were validated by comparing a simple uniform beam with other references. It was concluded that، for models without control system، small variation in mass distribution or section properties can cause significant changes in critical follower force، and also could change the characteristics of the instability from static to dynamic or vice versa. For beams with control system، the conjunction of the first non-zero frequency with the horizontal axes was remained almost fixed for different IMU locations and control gains. However، the system behavior and the characteristics of the instability depended on the IMU location and the control gains. Finally، the effects of the variation in diameter ratios on the critical controlled follower forces were studied and presented in this paper.