Abstract
Thispaperpresentsdynamicandstaticinstabilitycharacteristicsofafree-freemulti-steppedTimoshenkobeamsub-jected to a follower force, where each step has a point mass with transverse and rotary inertia. A finite element code isdeveloped to model two-dimensional multi-stepped Timoshenko beams using the extended Hamilton’s principle. Theeffects of each section parameters on the type of instability and critical follower force have been studied for differentmodelsofmulti-steppedbeams.Itisconcludedthattheassumptionofauniformbeamtostudymostaerospacestructuressuch as launch vehicles could lead to an unrealistic instability analysis, where any small change in the characteristicsparameters for each step could change the instability behavior significantly. Furthermore, this paper introduces a newparametric approach concept for analyzing the characteristics effects of a multi-step aerospace structure.Key Words: Multi-Stepped Timoshenko Beam, Follower Force, Finite Element, Static and Dynamic Instability
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