Free vibration and buckling characteristics of functionally graded beams with triply periodic minimal surface architecture

This work presents models to studies the free vibration and buckling characteristics of functionally graded porous (FGP) beam with triply periodic minimal surfaces including Primitive, Diamond, IWP, and Gyroid using Euler's beam theory. The models take into account the effect of the neutral axis dislocation during both vibration and buckling mode. The porous density is considered to be functionally graded along the vertical direction following the practical fabrication of architected structures. The effective stiffness is proposed in form of the three-degree polynomials and their coefficients are found by fitting the discrete data from three-dimensional finite element method (3D FEM) simulation of architected TPMSs with a wide range of porosity. The condition of gradient index is derived based on the power rule to make this work practical. 3D FEM simulations for FGP beam are carried out to validate against the present model in terms of natural frequency and neutral axis deviation to mid-plane with good agreements observed. It is found that three-degree polynomial is a good form to express the effective stiffness over the large range of porosity. In addition, the gradient index, beam dimension, architected material types, and base materials are found to affect significantly the free vibrational and buckling behaviors of beam.