Free vibration of the FG-GPLRC plates resting on an elastic foundation using the moving Kriging meshfree method

Abstract

The paper’s main purpose is to analyze the free vibration of graphene platelet-reinforced functionally graded metal foam plates using the C⁰-type higher-order shear deformation theory (C⁰-HSDT) with seven variables and the moving Kriging meshfree method (MKMM). Various types of porosity and graphene platelets distributions through the plate’s thickness are investigated in this study. Material properties of metal foam plates reinforced with graphene platelets are described using the Halpin-Tsai model. By applying Hamilton’s principle alongside the C⁰-HSDT, the governing equation for free vibration in functionally graded metal foam plate reinforced with graphene platelets is formulated and solved by the moving Kriging meshfree method. The accuracy of the computational model is verified by comparing the vibrational frequencies calculated in this paper with available results from the literature. Following this, the influences of porosity distributions, GPLs distributions, porosity coefficients, GPLs volume fraction, and geometric parameters on vibrational characteristics are examined, thereby contributing to the development of lightweight structures, advanced materials, and structural optimization for specific applications.