Based on the previous research of pounding tuned rotary mass damper （PTRMD）， a multiple pounding tuned rotary mass damper （MPTRMD） is proposed， which can be distributed and installed in the prefabricated cavity of the hollow floor slabs.This arrangement of MPTRMD is designed to take advantage of the cavity of the hollow modules thus avoiding extra spatial occupation of the dampers and maintaining the original layouts and functions of the structures. Moreover， this damping method is flexible to be installed in both horizontal and altitude directions of the structures according to the practical needs of the engineering applications. The device separates the practical mass of a single oscillator into multiple lightweight dampers， making it technically possible for the miniaturization and the application of the dampers with large additional mass. The dynamic equation of the controlled system with MPTRMD is derived， and its vibration reduction performance is also studied. The results show that the proposed MPTRMD has strong energy dissipation capacity and can effectively reduce the dynamic responses of the structure with different control schemes. The analysis about the number of dampers split shows that after the PTRMD vibrator is split， the control effect of the damper is rapidly improved when the number is small at the beginning， but with the further increase of the number， after reaching a certain degree， the lifting capacity slows down and has a downward trend， shows that there is an optimal interval.