Abstract
The equation of motion in matrix form of a cantilever Euler beam subject to a tipconcentrated follower force at the free end is formulated based on the Lagrangian approach and the assumed mode method. The non-conservative nature of the system is identified by the non-symmetric matrix in the equation of motion. The beam is assumed to rest on an intermediate spring support. Jump phenomenon for the critical follower load is found to occur for both variations in the support location as well as the stiffness of the spring support. Detailed history of the changes in the load-frequency diagram due to variation in the support location and the stiffness of the spring support is presented to explain the occurrence of the jump phenomenon. An interesting finding is that the rod is found to be extremely unstable for a certain combination of spring stiffness and support location for a cantilever rod.
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