Effects of damping on the dynamic stability of a rod with an intermediate spring support subjected to follower forces

Abstract

The equation of motion in matrix form of an Euler beam, including the effect of internal damping subjected to non-conservative follower forces, is formulated based on Lagrangian approach and the assumed mode method. The beam is assumed to rest on an intermediate spring support of large stiffness modeling a rigid support. The effect of slight damping on the jump phenomenon for the critical follower load with respect to variation in the support location is examined for a specific example of a simply supported-free rod. For some cases, the modes of instability in the form of flutter or divergence without damping are found to be unaffected by the presence of slight damping, although there may be a sharp decrease in the first critical load for instability by flutter. However, for specific locations of the intermediate spring support, the presence of a small amount of damping may change the mode of instability from divergence to flutter with a sharp decrease in the critical follower load. An interesting finding is that this mode of instability by flutter only occurs for an isolated and narrow range of follower loads.