On the Vibrations of Functionally Gradient Porous Shells

Abstract

In this work, forced vibrations of functionally gradient (FG) porous shell subjected to dynamic load is presented. The mechanical properties of the FG shell are graded smoothly in the thickness direction and they are assumed to be porosity dependent. The governing equations are obtained using a finite element formulation with the consideration of the transverse shear strains. The resolution procedure is carried out via the Newmark’s integration technique. The accuracy of the formulation is verified by comparing the present natural frequencies of the first four modes of vibrations with the existing studies in the literature. The effects of material compositions like porosity volume fraction, types of porosity distribution patterns and FG power index on time-deflection response of FG porous shell are also presented. The results show that the increase in porosity volume fraction and power FG index induces an augmentation in temporal deflections of the FG shell due to the reduction in the stiffness of the shell. Furthermore, the type of porosity distributions, namely even and uneven types, has a significant role on the dynamic behaviour of FG porous shell, because the uniform distribution of the pores, in even case, diminishes further the flexural rigidity of the shell compared to randomly distribution of the pores, in the case of uneven porosity distribution.