Variable Velocity Influence on the Vibration of Simply Supported Bernoulli - Euler Beam Under Exponentially Varying Magnitude Moving Load

Abstract

The variable velocity influence on the vibration of a simply supported Bernoulli-Euler beam, resting on a uniform foundation, under the action of an exponentially varying magnitude load moving with variable velocity is investigated in this work. The technique is based on the Finite Fourier Sine transformation and the Finite Difference method. Numerical results in plotted curves are presented. It is observed from the plotted curves that, when the foundation modulli ‘K’ and the axial force ‘N’ are fixed, the transverse deflections of the beam under load moving with variable velocity are higher than the deflections when the load moves with constant velocity. It is also observed that the response amplitudes in both cases of variable velocity and constant velocity decrease both with increasing ‘K’ and with increasing ‘N’. Also, the analysis shows that the effects of the foundation modulli ‘K’ and the axial force ‘N’ are more pronounced in the vibration of the beam under load moving with variable velocity than in the case when the load moves with constant velocity, hence more reinforcement is needed when the load moves with variable velocity.