<p>The dynamic response analysis and vibration suppression of multi-span beams are more aligned with practical engineering scenarios and entail a greater demand for vibration suppression solutions than those of single-span beams. In this paper, Hamilton’s principle and the assumed mode method (AMM) are employed to establish the equation of motion of the multi-span beam with tuned mass dampers (TMDs) under moving loads. The natural frequencies of the multi-span beams are calculated and show excellent agreement with those obtained from numerical results using finite element analysis. A three-span beam with TMDs is employed as a case study in which parameters such as the TMD mass ratio, frequency, damping ratio, and quantity are comprehensively considered to investigate its vibration suppression effects under moving loads. Meanwhile, the influences of moving load velocity and the number of beam spans on vibration characteristics of the multi-span beam are thoroughly investigated. It is noteworthy that the whale optimization algorithm (WOA) is applied to the vibration suppression of multi-span beams and successfully determines the optimal damper control strategy. The present results are helpful for the dynamic analysis and design of multi-span beams with TMDs under moving loads.</p>