A moving Kriging meshfree vibration analysis of functionally graded porous magneto-electro-elastic plates reinforced with graphene platelets

This article introduces a moving Kriging (MK) meshfree approach for studying the free vibration analysis of functionally graded porous magneto-electro-elastic plates with graphene platelet reinforcement (FGP-MEE-GPL). Functionally graded porous (FGP) plates are valued for their customizable material properties, while graphene platelets (GPLs) improve their mechanical performance. The pores are distributed in three patterns: uniform, symmetric I, and symmetric II. Similarly, GPLs are also arranged in three distribution patterns across the plate thickness. The structural characteristics of open-cell metal foam are used to establish the correlation between Young's modulus and mass density, providing a more accurate representation of the material's properties. The governing equations for the FGP-MEE-GPL plate are derived using the principle of virtual work and the higherorder shear deformation theory. The MK meshfree method is suggested for approximating the displacement, electric, and magnetic fields. The MK meshfree method offers an efficient solution for analyzing the vibration of the FGP-MEE-GPL plate, seamlessly addressing complex geometries and multi-field coupling without the necessity of mesh generation. The proposed model is validated by comparing its results with the reference's solutions. Parametric studies explore the influence of the porous coefficient, porous and GPLs distributions, initial external load magnetic and electric loads, and geometry on the FGP-MEE-GPL plate's vibrational frequency.