Nonlinear dynamic buckling of functionally graded porous beams

This article studies nonlinear dynamic buckling of imperfect beams made of functionally graded (FG) metal foams subjected to a constant velocity with various boundary conditions. Four types of FG porosity patterns, including two symmetric porosity distributions, non-symmetric porosity distribution, and uniform porosity distribution, are considered. By introducing the first mode function as a trial function, the Galerkin method is utilized to transform the governing equations into ordinary differential equations, which were then solved by the fourth-order Runge-Kutta method. The proposed methods are validated by using finite element method (FEM) and finally a detailed parametric study is conducted.