Vertical accelerations of simple beams due to successive loads traveling at resonant speeds

In this paper, the vertical acceleration response of a simple beam traveled by a series of equally spaced moving loads at constant speeds is studied by the superposition method. From the closed-form solution derived, the key parameters dominating the resonant response of the beam are identified, along with the effect of higher modes of vibration on the acceleration response investigated. For the loads moving at resonant speeds, the higher modes can have significant influence on the acceleration amplitude. This is true especially for beams with light damping, for which the maximum acceleration on the beam depends on which vibration mode is excited. As such, the maximum acceleration of the beam need not occur at the mid-point. By considering the resonant speeds associated with the first and second modes, a simplified formula is proposed for checking whether the maximum acceleration may occur at the mid-point of the beam. For the case when the structural damping is taken into account, the contribution of higher modes to the acceleration response tends to be damped out. It is concluded that for a beam properly damped, the maximum acceleration response of the beam is dominated by the fundamental vibration mode.