Cancellation of resonance for elastically supported beams subjected to successive moving loads: Optimal design condition for bridges

Abstract

This paper investigates comprehensively the resonance and cancellation conditions for the free vibration of elastically-supported (ES) beams subjected to successive moving loads. Focus is placed on application of the cancellation condition to minimize bridge vibrations, considering particularly the effect of elastic supports. In terms of the modal amplitude R of free vibration of the ES beam, both resonance and cancellation conditions are identified. This paper is featured by the fact that the cancellations are classified into two types as the external (load-related) and internal (structure-related) ones. Through the (internal) cancellation function, the criterion for selecting the optimal support stiffness ratio (SSR) is derived for the first time for suppressing the resonance of short to medium-span railway bridges. It depends solely on the bridge/vehicle length ratio L/d, and can be utilized to achieve near-perfect cancellation. The theoretical findings are validated by the finite element method (FEM) for various parameters. The results reveal that for beams with lengths in the ranges of (0.5d, d] and (1.5d, 2d], an SSR closer to the lower bound of the acceptable range should be selected to achieve the best effect. And for beams with lengths in the range of (d, 1.5d], the SSR should be selected as close to the optimal value as possible. Besides, it was found that damping in the beam and supports contributes to further suppression of vibration for bridges designed with optimal SSR.