Free vibrations and the stability of a geometrically non-linear column loaded by a follower force directed towards the positive pole

A slender system, built as a geometrically non-linear system and subjected to specific load by a follower force directed towards the positive pole, is discussed. The load is induced by heads composed of circular-profile elements. The problem of stability and free vibration was formulated on the basis of Hamilton’s principle and then, owing to its non-linearity, solved using the straightforward expansion method. This paper provides example results of numerical computations concerning the influence of selected parameters characterizing the considered column (including pre-stressing) on the stability and free vibration. The accuracy of the adopted mathematical model is also proved on the basis of experimental studies.