Influence of boundary conditions on the stability of a column under non-conservative load

Abstract The cantilever follower force problem with external damping is extended to a three-parameter case, including a concentrated mass, a linear elastic spring, and a partial follower force at the free end. As a result of the study an unexpected, hitherto unrecognized feature of stability/vibration is identified. Normally, the boundary conditions have great influence on the stability limits. However, it is proved that there exists a force at which the critical frequency is independent of all three boundary parameters. The characteristics of this force/frequency combination are discussed in detail, especially in relation to the corresponding eigenfunctions. Also a direct study of the onset of flutter as a function of the boundary parameters is included.