Free vibration analysis of functionally graded triply periodic minimal surface plates using a first order shear deformation theory and meshfree method

Abstract

This paper explores a free vibration analysis of functionally graded triply periodic minimal surface plates using a first order shear deformation theory in conjunction with moving Kriging meshfree method. The FG-TPMS plates are modeled the same as porous structures with three different patterns (Primitive, Gyroid, and wrapped package-graph) and six different volume distributions for each pattern. Employing a fitting method based on a two-phase piece-wise function, the mechanical properties of the FGTPMS plates are determined. The governing equations for the FG-TPMS plates are established using the virtual work principle and subsequently solved using the moving Kriging meshfree method. The study encompasses FG-TPMS square and circular plate, examining the natural frequency of the FG-TPMS plates with various length-to-thickness ratios, TPMS types, volume distributions, and boundary conditions.