Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element

The present paper aims at the study of the dynamic behavior of functionally graded carbon nanotubes-reinforced composite shell structures (FG-CNTRC) via forced vibration analysis. The governing equations of motion are developed using a linear discrete double directors finite element model. The elaborated model is based on high-order-distribution of displacement field and uses a cubic variation of the vector position along the thickness direction. A zero transverse shear stress at top and bottom surfaces is also imposed. Four types of distributions of carbon nanotubes (CNTs) such that uniformly and three functionally graded distributions are considered. The extended rule of mixture is used to estimate the effective material properties of carbon nanotube-reinforced composite (CNTRC) shell. The applicability and the performance of the present model are illustrated by three numerical examples of FG-CNTRC square plates, spherical caps and annular ring plates. The transient center deflections of the studied shell structures are computed and depicted for different volume fractions and profiles of CNTs, various boundary conditions and other geometrical parameters in order to show the effect of these parameters on dynamic behavior of FG-CNTRC shells.