An Influence of the Longitudinal Spring Element on Free Vibrations of the Partially Tensioned Column

In this paper the slender system subjected to Euler's load which is partially tensioned is considered. On one of system's ends the discrete element in a form of translational spring which limits the longitudinal displacement was used. The boundary problem of free vibration of the considered system was formulated on the basis of Hamilton's principle and solved according to the small parameter method due to nonlinearities. In the boundary problem formulation process the Bernoulli-Euler theory was used. The relationships between free vibration frequency and parameters such as external load magnitude, translational spring stiffness used for longitudinal displacement control and external load location were studied.