Propagation characteristics of lamb waves in a functionally graded material plate with periodic gratings

The propagation characteristics of Lamb waves in a functionally graded material (FGM) plate with periodic gratings have been studied. The power series technique is employed to solve the governing differential equations with variable coefficients. In the propagation direction, the displacements of Lamb waves are expanded in the Fourier series due to the periodicity of the structure. The convergences of the power series and Fourier series are proved and the method presented in the article is verified by the finite element method (FEM). The band gaps are obtained by the couplings between the different modes of Lamb waves induced by FGM. The effects of the structural parameters (such as the periodicity, mass, and length of the gratings) and gradient coefficient on band gaps are investigated. Numerical results show that the band gaps shift up as the gradient coefficient increases and the second band gap (SBG) is closed when the gradient coefficient is large enough. The conclusions are of practical significance for designing elastic wave filters with high-performance.