Lamb wave band gaps in a double-sided phononic plate

In this paper, we report on the theoretical investigation of the propagation characteristics of Lamb wave in a phononic crystal structure constituted by a square array of cylindrical stubs deposited on both sides of a thin homogeneous plate. The dispersion relations, the power transmission spectra, and the displacement fields of the eigenmodes are studied by using the finite-element method. We investigate the evolution of band gaps in the double-sided phononic plate with stub height on both sides arranged from an asymmetrical distribution to a symmetrical distribution gradually. Numerical results show that as the double stubs in a unit cell arranged more symmetrically on both sides, band width shifts, new band gaps appear, and the bands become flat due to localized resonant modes which couple with plate modes. Specially, more band gaps and flat bands can be found in the symmetrical system as a result of local resonances of the stubs which interact in a stronger way with the plate modes. Moreover, the symmetrical double-sided plate exhibits lower and smaller band gap than that of the asymmetrical plate. These propagation properties of elastic or acoustic waves in the double-sided plate can potentially be utilized to generate filters, slow the group velocity, low-frequency sound insulation, and design acoustic sensors.