Lamb wave band gaps in a homogenous plate with periodic Gaussian surfaces

Abstract

The Lamb wave band structure of a one-dimensional thin plate with periodic Gaussian surfaces is calculated based on the eigen-mode matching theory (EMMT) method. The finite element method is also employed to calculate the transmission power spectra and the band structure, which are both in good agreement with the results of the EMMT method. In contrast with the straight stubs, the low-frequency band gap of the system with the Gaussian surfaces is wider, when the Gaussian domain's height and area are equal to those of the stub, and the two systems' main plate size and materials are the same. This can be confirmed by the ‘spring–mass' model, which can be used to estimate the resonant frequency. We also investigate the effects of the geometrical parameters on band structure, including the height of the Gaussian domain, the plate thickness and the filling fraction. The results suggest that the band gaps have a close relevance to them.