This research examines the natural vibration analysis of magneto-electro-elastic functionally graded porous (MEE-FGP) plates. The study employs a moving Kriging (MK) meshfree method to analyze the MEE-FGP plates composed of piezoelectric and piezomagnetic materials with both even and uneven distributions of porosity. The electric and magnetic potentials in the three-dimension are assumed to follow a combination of cosine and linear variations in the thickness direction to satisfy the Maxwell equations in the two-dimension. The displacement field, electric potential and magnetic potential are approximated by the MK interpolation shape function, which satisfies the Kronecker's delta property. This property allows to impose directly essential boundary conditions as those in the finite element method. The governing equilibrium equations are derived using a C⁰-type higher-order shear deformation plate theory (C⁰-HSDT) in conjunction with the virtual work principle and then solved using the MK meshfree method. Various geometries are performed to determine the natural frequency of MEE-FGP plates. The impact of the porosity distribution, porosity volume fraction, volume fraction index, initial external electric voltage, initial magnetic potential and geometry on the natural frequency of the MEE-FGP plates is fully investigated. Numerical results provide an effective approach to analyze and calculate the natural vibration of MEE-FGP plates.

本研究检查了磁电弹性功能梯度多孔 (MEE-FGP) 板的自然振动分析。该研究采用移动克里格 (MK) 无网格方法来分析由压电和压磁材料组成的 MEE-FGP 板，孔隙率分布均匀和不均匀。假定三维中的电势和磁势在厚度方向上遵循余弦和线性变化的组合以满足二维中的麦克斯韦方程。位移场、电势和磁势由满足Kronecker's delta性质的MK插值形函数近似。此属性允许直接施加基本边界条件，如有限元方法中的边界条件。⁰型高阶剪切变形板理论（C ⁰ -HSDT）结合虚功原理，采用MK无网格法求解。执行各种几何形状以确定 MEE-FGP 板的固有频率。充分研究了孔隙率分布、孔隙率体积分数、体积分数指数、初始外部电压、初始磁势和几何形状对 MEE-FGP 板固有频率的影响。数值结果为分析和计算MEE-FGP板的自振提供了一种有效的方法。