Effect of the internal rib structure of the inclusions on the two-dimensional phononic crystal composed of periodic slotted tubes in air

Using a finite element method based on the Bloch theorem, a new phononic crystal composed of periodic slotted tubes with internal rib structure in air is investigated. Two parallel plates with slit are introduced into the inclusion as the internal rib structure and its effect on band gaps is studied. The band structure and acoustic modes of the PC are calculated. Results show that the starting frequency of the first band gap is rather lower than that of slotted tubes without rib structure. The internal rib structure plays an important role in both the lower and upper edges of the first band gap. Some rib structural parameters are also studied for their effects on the first band gap. Results show that the first gap can be modulated widely by these parameters and the Helmholtz resonator theory can be used to explain the relationship between the band gap and the parameters.