Dynamic Analysis of Functionally Graded Porous Beams Using Complementary Functions Method in the Laplace Domain

Abstract

In this study, an efficient numerical procedure is introduced to the solution of the dynamic response of functionally graded porous (FGP) beams. The elastic modulus and mass density of the porous materials are considered to have non-uniform distributions along the thickness direction. The typical open-cell metal foam is assumed to govern the material constitutive law. Within the framework of the first-order shear deformation theory (FSDT) the influence of shear strain is included in the formulations. The impact of damping is also considered. By using the canonically conjugate momentums and their derivatives, the governing canonical equations of motion of FGP beams are derived for the first time. These equations are then transformed into the Laplace space and solved numerically with the aid of the Complementary Functions Method (CFM). Obtained results are retransformed to the time domain by using an efficient inverse transform method. The dynamic response of FGP beams is studied for several boundary and loading conditions. The suggested procedure is verified with the available published literature and the finite element method. Detailed parametric studies are conducted to show the influence of porosity constants, symmetric and asymmetric porosity distributions and damping ratios on the dynamic response of FG porous beams.