Dynamic stability of a rod with an intermediate spring support subject to subtangential follower forces

Abstract

The equation of motion in matrix form of an Euler beam subject to a tip-concentrated subtangential follower force is formulated based on Lagrangian approach and the assumed mode method. The beam is assumed to rest on an intermediate spring support. The critical flutter load is first computed for a simply supported-free rod on an intermediate spring support of large stiffness modeling a rigid support. Convergence of the smallest critical load is found to be fast with just five terms for the assumed deflection function. Jump phenomenon for the critical follower load is found to occur for both variations in the support location, the stiffness of the spring support, as well as the parameter for subtangentiality. Detailed history of the changes in the load-frequency curves due to variation in these parameters is presented to explain the occurrence of the jump phenomenon. In respect of changes in the parameter for subtangentiality for a rod on an intermediate spring support, it is found that the rod can undergo multiple transition from divergence to flutter, and then back to divergence when the subtangentiality changes from zero to unity.