Because the structural vibration in rail transit has a deep impact on safety and environment, in order to control the vibration of the plate structure, the amplitude-enhanced device can be used to increase the stiffness and mass of the vibration absorber, and the amplitude-enhanced vibration absorber is periodically arranged on the plate. Based on the null space method and the energy method, a new band gap calculation method is improved, which overcomes the difficulty of constructing the shape function under the periodic boundary condition, and greatly improves the calculation efficiency. Using this method, the band gap characteristics of a plate with periodically attached AMVAS are studied. The vibration mode law of the starting and ending points of the band gap are studied, and the influence of the amplification coefficient and mass ratio of the amplitude enhancement device on the band gap is discussed. In addition, the vibration transmissibility of periodic plate structures with amplitude-enhanced vibration absorbers and ordinary vibration absorbers is compared and analyzed. The results show that the appropriate amplification factor and mass ratio can effectively enhance the low frequency vibration reduction effect of the device. The amplitude enhanced vibration absorber has the effect of increasing the attenuation amount and broadening the attenuation range, and has a significant effect on the vibration control of the specific frequency of the periodically arranged plate structure. The research results can provide theoretical basis for vibration and noise reduction in the field of rail transit.