Enlargement of the locally resonant Lamb wave band gap of the phononic crystal plate at the deep sub-wavelength scale

Abstract

In this paper, the numerical investigation of Lamb wave propagation in two-dimensional phononic crystals composed by depositing the heavy cylinder stubs squarely onto both sides of a composite thin plate is presented. A significant enlargement of the relative bandwidth by two orders of magnitude compared with two-dimensional binary locally resonant phononic crystal plates and one order of magnitude compared with both the ternary composite plate and the simple plate with stub structures at deep sub-wavelength scale is obtained and discussed. Based on an efficient finite element method, we show that this band gap enlargement is due to the coupling between the plate mode and ‘double mass-spring’ mode, which leads to the enhancement of the locally resonance mechanism. The calculated elastic wave displacement fields illustrate the physics mechanism of opening the low frequency band gap and the existing of the flat bands. We also found that both the band gap and the flat bands depend on the geometry parameters of the heavy stubs and composite plate significantly.