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

• Published in: International journal of solids and structures Vol. 45; no. 1; pp. 87 - 112
• Main Authors: Tomski, L., Uzny, S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 2008
• Subjects: Divergence instability; Elastic columns; Natural transverse frequency; Elastic columns; Divergence instability; Natural transverse frequency
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2007.07.011

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.