Large band gaps in two-dimensional phononic crystals with neck structures

In this paper, we study the band gap properties of a two-dimensional phononic crystal composed of periodic cylinders embedded in a homogenous matrix. The cylinders are not connected with the matrix directly but linked with it through the neck structures constituted by part of a circle. The dispersion relations, transmission spectra, and displacement fields of the eigenmodes of this phononic crystal are studied using the finite-element method. In contrast to the typical phononic crystals where the cylinders and matrix are in contact completely, the proposed structures with necks display larger band gaps at lower frequencies. The reason for the occurrence of the low-frequency band gaps as well as the effects of the geometrical parameters of the neck structures on the gaps are further explored numerically. Results show that the openings of the band gaps are attributed to the resonance of the cylinders and the interaction between the cylinders and the matrix, resulting from the introduction of the necks. The band gaps are significantly dependent upon the geometrical parameters such as the rotation angle of the necks which is defined as the angle between the centerline of the neck and the x-axis, the arc length of the necks, and also the filling ratio of the inclusions. The study in this paper is relevant to the design of tuning band gaps and isolators in the low-frequency range.