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

Abstract

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.

Instability and vibration of multi-member columns subjected to Euler’s load

“…The research on this phenomenon has been done by Sokół [25], Tomski and Uzny [28,29] and Tomski and Szmidla [30].…”

“…At this point the results of the monitoring are done on the basis of the analysis of the characteristic curves (curves on the plane natural vibration frequency-external load). Leung [16], Sokół [25], Tomski and Uzny [28,29], Tomski and Szmidla [30] and shape modes. The bifurcation load magnitude at which the instability occurs is also presented for each configuration.…”

“…(8)] the small parameter method has been used [28,29,31]. In this paper only the rectilinear form of static equilibrium is investigated.…”

Numerical studies on stability of slender supporting structures

“…The presence of both forms depends on the magnitude of the applied external load. Many scientific papers can be found where the phenomenon of the change of the static equilibrium form takes place along with the presence of the local and global instability regions (see [11,12]). The external load is being realized by means of an axially applied external force with a constant line of action (Euler's load).…”

Vibration control of a column with concentrated mass on by means of piezoceramic elements

“…The study on vibration and instability of slender systems subjected to different types of external loading were performed by many scientists [5][6][7][8]. They have investigated the influence of the geometrical and physical features on dynamic behavior of columns and beams.…”