Abstract: A mid- and low-frequency broadband side branch pipe muffler with small size is designed. At first, a mathematical model is established to describe acoustic transmission losses of a side branch pipe muffler by using the transfer matrix method, and the side branch pipe mufflers with preset resonance frequencies are designed; then the influences of structural parameters of the mufflers on transmission loss are analyzed, and a side branch pipe unit is subsequently determined based on the analyses. Next, periodic structures are formed by arraying the units along the axial or circumferential directions of the main propagation path of acoustic wave, and the influence of periodicity on noise reduction is studied. Finally, side branch pipe units with different resonant frequencies are combined to build a periodic structure with an effective bandwidth of 493-3 033 Hz, meanwhile, side branch pipes are bended to reduce structural sizes. The results show that, the number of axial branching period does not affect the resonant frequency of the structure, but, with the increase of the number of circumferential branching period, the resonant frequency will shift to high frequencies, and the shift amplitude will gradually slow down; the increase of the numbers of axial branching and circumferential branching periods can significantly extend the effective bandwidth; bending side branch pipes can reduce structural sizes and has little influence on structural acoustic characteristics; a mid- and low-frequency broadband muffler can be obtained by the integrated utilization of the structures with different axial branching and circumferential branching periods, as well as by combining the side branch pipe units with different resonance frequencies.