Band Structures in Two-Dimensional Phononic Crystals with Periodic S-Shaped Slot

Band structures are investigated in two-dimensional phononic crystals (PC) composed of a periodic S-shaped slot in an air matrix with a square lattice. Dispersion relations, pressure fields and transmission spectra are calculated using the finite element method and Bloch theorem. Numerical results show that the proposed PC can yield complete and large band gaps at lower frequency ranges compared with that of the Jerusalem slots in Li et al. (Phys B 456:261–266, 2015) under the same parameter setting of the lattice and outline of the inclusions. The transmission spectrum is verified to be reasonably consistent with the band gaps along the $$\Gamma X$$ΓX direction. By analysing the pressure fields of several modes, the resonance modes of cavities within the S-shaped slot structure are found to result in the low-frequency band gaps. The effects of the geometrical parameters on the upper and lower edges of the first and second complete band gap are further studied. Numerical results show that the bandwidth of the first and second band gaps can be modulated over an extremely large frequency range by the geometrical parameters. The properties of the proposed PC have potential for implementation in structures and devices of noise and vibration control, such as noise filters and waveguides.