Dynamic Behavior of Elastic Beam Including Effects of Axial Force

Abstract

This paper deals with the nonlinear vibration of a simply supported beam subjected to a sinusoidally distributed impulsive load, and then of the beam with simply supported or clamped ends under a uniform impulsive load, using the Galerkin method. The resulting equations for the mid-span deflection f(t) are solved in closed forms, using Jacobis' elliptic function. The solutions show that the effects of the axial force are large, comparing with solutions of the linear vibrations.
Furthermore, the problem of the transverse impact of a mass on a beam with simply supported or clamped ends is treated by using the difference method. These results show the similar tendency to the transverse vibration and the impulsive time becomes shorter as the impulsive velocity becomes large. Although the axialinertia effects are taken into account in this case, they are shown to be negligibly small.