The effect of internal axial forces of a cantilever beam with a lumped mass at its free end

When a cantilever beam with a lumped mass at its free end undergoes free transverse vibration, internal axial forces are produced in the beam. Such internal axial forces have an effect on free transverse vibration of the beam. This effect is studied in this paper. The equations of motion for the beam in terms of the generalized coordinates including the effect are derived. The method for determining free transverse vibration of the beam including the effect is presented. In numerical simulations, the results of free transverse vibration of the free end of the beam including and not including the effect are obtained. Based on comparison between the results obtained, the conclusions concerning the effect are given.