Study on bandgap of a novel phononic crystal with low-frequency sound insulation

To solve the problem of low-frequency noise in the environment, a two-dimensional Helmholtz-type phononic crystal with a labyrinth tube was designed in the paper. First, the low-frequency band structure was calculated by the finite element method (FEM) and transfer matrix method (TMM). Second, the bandgap formation was analyzed by using an acoustic pressure field, and the “spring-oscillator” equivalent model of the structure was established. Finally, the influences of structural parameters on the first bandgap were investigated. Results show that there are four bandgaps in the frequency range of 0–300 Hz, and the lower limit of the first bandgap can be as low as 12.15 Hz, which improves the low-frequency sound insulation ability of phononic crystals of the same size. The calculation results of the two methods (FEM and TMM) are basically consistent. Research on the influencing factors of the bandgap shows that the increase in the length of the tube will reduce the upper and lower limits of the bandgap and narrow the bandgap width. With the increase of the lattice constant, the upper limit of the bandgap decreases, while the lower limit of the bandgap remains unchanged. The design provides a new method to solve the problem of low-frequency noise reduction.