The effect of the neutral point position on the natural frequencies of lateral vibrations of a hanging beam

Abstract

In this article, the effect of axial force variation by position, on the natural frequencies of lateral vibration of a hanging beam, is analysed for different boundary conditions. To this aim, the equations of motion are derived by writing the potential and kinetic energies of the beam, considering the non-linear coupling between the axial and lateral vibrations. These energy equations are discreted by the mode summation method. The effect of the neutral point position on the natural frequencies and the mode shapes of the linearized system are investigated. By increasing the end axial force, the beam's natural frequencies are reduced and, for a critical position of neutral point, the first natural frequency of the beam vanishes and the beam buckles.