Free Vibration of Functionally Graded Carbon Nanotube Reinforced Composite Lévy Conical Panels

Free vibration of functionally graded carbon nanotube reinforced composite (FG-CNTRC) Lévy conical panels is analyzed in this research. Distribution of the carbon nanotubes through the thickness of the panel may be uniform or functionally graded. Properties of thecomposite media are obtained by a refined rule of mixtures approach which contains the efficiency parameters. Hamiltons principle, using the first order shear deformation theory of shells with the Donnell type of kinematic assumptions, is utilized to drive theequations of motion and the associated boundary conditions. The Lévy type of conical shell with simply supported boundary conditions along the straight edges is considered. A semi-analytical solution based on the trigonometric expansion through the circumferentialdirection combined with the generalized differential quadrature (GDQ) discretization in longitudinal direction is developed. Solution method can be used for any arbitrary type of free, clamped, and simply supported boundary conditions along the two other curved edges of the shell. One comparison study are conducted to validate the present solution. Afterwards, parametric studies are developed to investigate the influences of boundary conditions, semi-vertex angle of the cone, and the volume fraction of CNTs