Lamb waves in two-dimensional phononic crystal slabs with neck structures

Abstract

In this paper, a new structure of two-dimensional phononic crystals consisting of one or more rows of parallel rectangular rods placed periodically in a homogenous slab, in which the rods are not connected directly but linked through neck structures with the slab, is proposed, and the Lamb wave propagation in this structure is investigated with numerical analysis. The dispersion relations and the power transmission spectra are studied using the finite-element method. In contrast to the phononic crystals where the rods and the slab are completely in contact, the proposed structure with necks are proved to display band gaps at much lower frequencies. The displacement fields of the eigenmodes of the band edges are computed and analyzed to clarify the mechanism for the generation of the low-frequency band gaps. It is found that the low-frequency band gaps are attributed to the interaction between the local resonance of the rod inclusion connected with the neck and the Lamb modes of the four plates which are formed by the introduction of the neck. Furthermore, the influences of the geometry parameters of the neck on the band gaps are discussed. Numerical results show that band gaps are significantly dependent upon the width and the position of the necks while insensitive to the neck length. These properties of Lamb waves can potentially be applied to optimize band gaps, generate filters, and design acoustic devices.