Effect of Variable Axial Force on the Vibration of a Thin Beam Subjected to Moving Concentrated Loads

Abstract

The effect of variable axial force on a loaded beam subjected to both constant and variable loads
are considered herein. The beam is assumed to be uniform, thin, and has a simple support at both
ends. The constant load moves with constant velocity and uniform acceleration. The Galerkin’s
method and the integral transformation method are employed in solving the fourth order partial
differential equation describing the motion of the beam – load system. On solving, results show
that, increase in the values of axial force N gives a significant reduction in the deflection profile
of the vibrating beam. Results also show that the addition of the axial force N, foundation
modulus K, and consideration of a damping effect in the governing equation increases the
critical velocity of the dynamical system, thus, the risk of resonance is reduced.