Vibration absorbers for simply supported beams subjected to constant moving loads

Abstract

Vibration suppression in simply supported beams traversed by constant moving loads is explored using linear vibration absorbers. Assuming the Euler–Bernoulli beam theory, the beam is modeled using its first ten modes. The problem is formulated in terms of dimensionless parameters to render the results generic which are obtained for a range of the beam modal damping ratios and the system mass ratio. The objective is to minimize the maximum beam displacement for all load speeds. It is shown that the optimal absorber is an undamped absorber which should be attached at a fixed location irrespective of the modal damping or mass ratios. The optimal stiffness ratio is calculated numerically and a convenient analytical expression is obtained by curve fitting the numerical results to a second-order polynomial. The maximum error between the analytical model and the numerical solution is found to be negligible. The results are validated through comparison with a numerical example which was considered in the literature.