Lamb wave band gaps in one-dimensional radial phononic crystal plates with periodic double-sided corrugations

In this paper, we present the theoretical investigation of Lamb wave propagation in one-dimensional radial phononic crystal (RPC) plates with periodic double-sided corrugations. The dispersion relations, the power transmission spectra, and the displacement fields of the eigenmodes are studied by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. Numerical results show that the proposed RPC plates with periodic double-sided corrugations can yield several band gaps with a variable bandwidth for Lamb waves. The formation mechanism of band gaps in the double-sided RPC plates is attributed to the coupling between the Lamb modes and the in-phase and out-phases resonant eigenmodes of the double-sided corrugations. We investigate the evolution of band gaps in the double-sided RPC plates with the corrugation heights on both sides arranged from an asymmetrical distribution to a symmetrical distribution gradually. Significantly, with the introduction of symmetric double-sided corrugations, the antisymmetric Lamb mode is suppressed by the in-phase resonant eigenmodes of the double-sided corrugations, resulting in the disappearance of the lowest band gap. Furthermore, the effects of the geometrical parameters on the band gaps are further explored numerically.