Vibration of simply supported beams under a single moving load: A detailed study of cancellation phenomenon

• A formula for free response, valid for lightly and heavily damped beams, is given.
• Investigation of cancellation mechanism in beams under single moving load is done.
• Cancellation is interpreted based on amplitude, phase and initial conditions.
• It is proved that when first mode cancels all higher modes also get cancelled.
• Effect of damping at resonant and cancellation speeds is predicted.

Dynamic behaviour of simply supported uniform beams subjected to a single moving point load is analysed in this paper. A simple closed-form expression for free vibration response, valid for both lightly and heavily damped beams, is formulated. A detailed investigation of the cancellations of free responses is carried out. New interpretations for the cancellation mechanism, from the perspectives of free vibration amplitude and phase angle, are presented. Expressions for cancellation speed ratios are formulated based on the initial velocity and displacement conditions for free vibration. The effect of damping on the cancellations of free responses is also studied.