Vibration and Stability of Geometrically Nonlinear Column Subjected to Generalized Load With a Force Directed Toward the Positive Pole

Abstract

Considered herein is the vibration and stability problems of a slender column subjected to generalized load with a force directed toward the positive pole. The load is developed by heads composed of circular profile elements. The geometrically nonlinear problem of stability and free vibrations is formulated on the basis of Hamilton's principle, and due to nonlinearity, the problem is solved by applying the small parameter method. Vibration and stability results show the influence of chosen parameters that characterize the considered column (including initial prestressing). The assumed mathematical model is validated by experimental results.

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.…”

Nonconservative stability of viscoelastic plates subject to triangularly distributed follower loads

“…More recent studies on nonconservative loading include columns subject to uniformly distributed follower loads by Kim (2010), Kim et al (2008) and Kazemi-Lari et al (2013) and to triangularly distributed follower loads by Kim (2011). The follower force can also be realized by means of properly shaped loading heads which can affect the displacements of the loaded end as studied by Tomski and Szmidla (2004) and Tomski and Uzny (2013b). The installation of Tomski's head can lead to a loading force which is tangent to the end of the column and can be conservative Uzny, 2008, 2013a).…”

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).…”