Forced Vibration Analysis of Functionally Graded Rectangular Plates with Porosities under a Moving Load

In this paper, vibration behaviors of functionally graded rectangular plates with porosity under a moving concentrated load are considered. Mechanical properties such as elasticity modulus and density of functionally graded (FG) plates are varied as power-law, while Poisson’s ratio is kept constant and porosity as two types of evenly distribution (porosity-I) and unevenly distribution (porosity-II) is assumed. Based on first order shear deformation theory (FSDT) and by employing Hamilton’s principle, the theoretical equations of motion and boundary conditions are derived. Dimensionless discrete equations have been achieved by using generalized differential quadrature method and Newmark procedure. The convergence and accuracy of the present formulation and method of the solution are demonstrated. The effect of volume fraction index, porosity volume fraction and distribution pattern on displacements of plates have been investigated. It is discovered that the volume fraction index has a significant effect on the deflection of the plates and the porosity volume fraction influences more significantly on deflection of porous FG plates in porosity-I than in porosity-II.