## 1 Introduction
[21] examined the effect of grading pattern and porosity on the eigen characteristics of FG porous structure using higher-order displacement kinematics. [PERSON] [22] presented a higher-order shear and normal deformation theory for the static analysis of porous thick rectangular plates by considering the thickness stretching effect. [PERSON] et al. [23] proposed a new quasi-3D hyperbolic SDPT for the bending and free vibration analysis of FG porous plates on elastic foundation. [PERSON] and [PERSON] [24] analyzed the large-amplitude free vibration of FG porous cylindrical panels considering different shell theories and boundary conditions. [PERSON] et al. [25] parametrically examined the wave propagation behavior in FG metal porous plates reinforced with graphene platelets with respect to the distribution of porosity and graphene. [PERSON] et al. [26] numerically explored the influence of porosity on static bending analysis of FG porous beams using a refined mixed FE beam model. Although many researchers studied the bending and free vibration responses of FG porous structures, the effects of porosity on these responses were not sufficiently investigated, particularly with regard to the combination of the material composition distribution, the porosity distribution, the width-thickness ratio, and boundary condition. Moreover, the numerical studies on FG porous structures mostly relied on the FEM. Therefore, deeper numerical investigation of these responses of FG porous structures using a reliable and effective meshfree method has significance. Motivated by this situation, the current study intended to deeply investigate the bending and free vibration responses of ceramic-metal FG porous plates using 2D NEM in the combination of abovementioned three parameters and to the boundary condition. As an extension of previous work [27; 28] on the NEM hierarchical models for plates and sandwich plates, this study combines 2D NEM, the (3,3,2) hierarchical model and the cosine-type porosity distributions. As a last introduced meshfree method, NEM shows high numerical accuracy, even for coarse grids, thanks to the high smoothness of its Laplace interpolation (\(L/I\)) functions. Moreover, it can effectively analyze 3D FG porous plates when it is incorporated with the hierarchical model, in which the displacement field is decomposed into the in-plane triple-vector function and 1D assumed thickness monomial. In this study, the static bending and free vibration problem is formulated using a third-order SDPT-like (3,3,2) hierarchical model and approximated by 2D NEM. The thickness-wise distributions of porosity and constituent materials are expressed by the cosine and power-law functions, respectively. The numerical method is demonstrated through the numerical experiment and verified by comparison with the existing reference solutions. As well, the central deflections and the fundamental frequencies of ceramic-metal FG porous plates are parametrically investigated for the magnitude and distribution of porosity, the ceramic gradation index, the width-thickness ratio, and the boundary condition. The present numerical results are help one understand and design ceramic-metal FG porous plates by considering the porosity.