Dynamic analysis of functionally graded porous structures through finite element analysis

A finite element method (FEM) analysis framework is introduced for the free and forced vibration analyses of functionally graded porous (FGP) beam type structures. Within the proposed computational scheme, both Euler-Bernoulli and Timoshenko beam theories have been adopted such that the explicit stiffness and mass matrices for 2-D FGP beam element through both beam theories are explicitly expressed. Both Young's modulus and material density of the FGP beam element are simultaneously considered as grading through the thickness of the beam. The material constitutive law of a FGP beam is governed by the typical open-cell metal foam. Furthermore, the damping effects of the FGP structures can be also incorporated within the proposed FEM analysis framework through the Rayleigh damping model. Consequently, the proposed approach establishes a more unified analysis framework which can investigate simple FGP beams as well as complex FGP structural systems involving mixture of different materials. In order to demonstrate the applicability, accuracy, as well as the efficiency of the proposed computational scheme, both FGP beams and frame structures with multiple porosities have been rigorously explored.