The two circular structures with local resonance resonant hammers proposed in this paper have the comprehensive performance of small size, easy fabrication and low frequency vibration and sound damping. In the study, Bloch’s theorem is used to calculate the energy band curves of the two structures and to analyze the vibration forms of the structures at the edge of the band gap. At the same time, the integrated analysis means of phase constant surface, group velocity and phase velocity are innovatively used to explore the real propagation path of waves and provide experience for topology optimization. The position of resonant hammers, the mirror symmetry structure and the size of resonant hammers are adjusted to optimize the band gap for both structures. Finally, the vibration transmission characteristics of the finite period structure are calculated to verify the band gap and evaluate the vibration isolation performance. The results show that the new structure has low-frequency noise reduction performance, and the band gap frequency can be further reduced by topology optimization. This study presents an innovative approach for achieving low-frequency noise reduction, analysis of wave propagation paths and lightweight design.