Determination of Critical and Cancellation Speeds of Euler–Bernoulli Beam Subject to a Continuously Moving Load

Treated herein is an elastic beam that is subjected to a constant load that travels continuously (back and forth) along its span. The dynamic deflection of the beam is investigated analytically so as to predict the critical and cancellation speeds. Closed-form solutions are obtained for the damped system for each load condition and superimposed to determine the total solution of the response. Unlike the classical case of load traveling at constant speed in one direction, multiple resonance peaks are observed for reciprocating load at speeds that are lower than the classical critical speed. It is also observed that resonance may not exist at the classical critical speed for simply supported beams due to the symmetry of the beam. The dynamic deflection is examined for simply supported beams to determine the speeds that cause amplification or cancellation of the free response. The current load condition may have possible application in view of its potential use for vibration suppression, as a moving vibration absorber, or for magnification, in energy harvesting. The results are interpreted in order to understand the variation of dynamic deflection and to estimate the critical speeds for different load conditions.