Flutter Stability Behavior of Free–free Column With A Movable Mass Subjected To Follower Drag Force

The stability behavior of a prismatic free–free column, carrying a movable mass and subjected to the action of follower end thrust and follower frictional resistance has been investigated. A finite element model of the beam is formulated using the modified Hamilton's principle. The eigenvalues of the characteristic equation of the governing differential equation of motion are extracted using the Q-R algorithm. The parameters considered in the investigation include: (i) ratio of the movable mass to the total mass, (ii) position of the movable mass, and (iii) ratio of resultant frictional drag to the magnitude of the end thrust. Some of the interesting results conducted in this study may be useful to the design engineers. Depending on the various parameters used, the column may lose stability either by divergence or by flutter. The first two frequencies vanish when the column is subjected to only an end thrust without any extra mass and/or frictional drag, indicating the occurrence of both the rigid body translation and rotation. However, only one vanishing frequency is observed when the column is carrying a movable mass and is subjected to a frictional drag (irrespective of their values), indicating the occurrence of only one rigid body motion.