This study presents a novel method for analyzing the vibration and noise from the periodic rib stiffened plate (PRSP). For the first time, the band gap theory was combined with hybrid finite element-boundary element method (FE-BEM) to predict the vibro-acoustic characteristics of this structure and guide its vibration and noise reduction design from the perspective of bending wave propagation. The excitation test was carried out simultaneously to verify the rationality and accuracy of the proposed method. Then, the acoustic contribution analysis was conducted and the influence of structural design parameters on bending wave bandgap and noise reduction effect was discussed in detail. The results show that there are alternating passbands and stopbands for bending waves propagating in PRSP, making the vibro-acoustic responses in different frequency bands exhibit distinct differences as well. Increasing the base plate thickness and decreasing the rib spacing are conducive to widen the bandgaps and reduce the noise radiation, which are the decisive factors affecting the vibro-acoustic characteristics of PRSP. While the rib thickness has little effect, this provides a new approach for vibration mitigation and acoustic optimization in steel bridges.