Analysis of Lamb Wave Dispersion Behavior in Functionally Graded Porous Plates Under Mixed Boundary Constraints

The dispersion behavior of Lamb waves in porous functionally graded materials (FGMs) plates under mixed boundary conditions is studied, and the influence of porosity on the dispersion behavior of Lamb waves in porous FGM is analyzed. First, the mixed power-law model is used to characterize the material properties of a porous FGM plate in the thickness direction. Second, based on the elastic wave theory, the wave equation in an infinite porous FGM plate is established, and then the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) method is used to obtain the dispersion equation of Lamb wave in porous FGM. The porous FGM plate is degenerated into an isotropic material, and the validity and correctness of the proposed method are verified by comparing with the existing literature results. Finally, the dispersion equation is solved by mathematical software, and the dispersion curves under different porosity, porous FGM plate thickness and material gradient index are obtained. The results show that the porosity, plate thickness and material gradient index have a significant effect on the dispersion of Lamb waves. This study provides a theoretical and numerical basis for understanding and applying the dispersion behavior of Lamb waves in porous FGM.