Wave propagation analysis in functionally graded metal foam plates with nanopores

In this paper, the influence of the surface effect on wave propagation characteristics in functionally graded metal foam plates (FGMFPs) with nanopores is studied, where different porosity distribution patterns are taken in account. The surface effect between pore and matrix in FGMFP is considered by the Gurtin-Murdoch surface elasticity model. The plate is divided into finite thickness layers along the gradient, and each layer of porous material is homogenized using locally exact homogenization theory. On the basis of obtaining the effective modulus of each layer of porous material, the governing equations of the plates are obtained by Hamilton's principle and different plate theories, upon which wave dispersion and phase velocity curves of FGMFP are obtained. The developed method is verified by comparing the wave dispersion curves against existing literature. Finally, the effects of different plate theories, porosity distribution, unit cell array, surface effect, pore radius and its distribution pattern, and graphene platelet weight fraction on the wave dispersion and phase velocity curves are systematically investigated. The results in this paper may provide guidance for the design of FGMFPs with nanopores.