Lamb wave band gaps in a homogenous plate with periodic tapered surface

Abstract

In this paper, we present the numerical investigation of Lamb wave propagation in a homogenous plate with periodic tapered surface, which gradually increases the width from the lower base to the upper base. 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 effects of the geometrical parameters (including the ratio of the lower base width to the upper base width, and the ratio of the upper base width, the thickness of the tapered surface, and the thickness of the homogenous plate, respectively, to the lower base width) on the band gaps. Numerical results show that the band gaps can be effectively shifted by changing the geometrical parameters. Especially, the width of the first band gap changes approximately linearly by changing the ratio of the upper base width to the lower base width and in return. The transmission bands of the structure with the tapered surface are more flat than those of the structure with the stubbed surface. Moreover, the proposed homogenous plate with periodic tapered surface exhibits lower and smaller band gap than that of the homogenous plate with periodic stubbed surface due to weak localized resonance of the tapered surface with the upper base wider than the lower base. These properties of elastic or acoustic waves can potentially be utilized to tune band gaps, slow the group velocity, generate filters, and design acoustic sensors.