The acoustic radiation of 2D nearly periodic plates interacting with light fluids is addressed. Metamaterial plates made up of resonant multi-layered cells/substructures with varying (random) geometrical properties, which are described via distorted finite element meshes, are dealt with. The proposed approach involves the Craig-Bampton method and an interpolation scheme for modeling the substructures and approximating the related reduced mass and stiffness matrices. In this paper, this approach is applied to compute the radiation efficiencies of such metamaterial plates with the method of elementary radiators. The relevance of the proposed approach is highlighted through numerical experiments. Especially the structural and acoustic responses of a nearly periodic plate are assessed and compared to the purely periodic case.