Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes

This study investigates the static and free vibration behavior of rotating functionally graded (FG) truncated conical shells reinforced by carbon nanotubes (CNTs) with a gradual distribution of the volume fraction through the thickness. CNTs are here selected as reinforcement, because of their noteworthy physical and chemical properties, together with their ability to enhance the mechanical properties of the whole composite structure. A two-parameter agglomeration model is considered to describe the micromechanics of such particles, which tend to agglomerate into spherical regions when scattered in a polymer matrix. From the macro-mechanical point of view, the conical structures are characterized by a gradual variation of their mechanical properties along the thickness direction, since different distributions are explored to describe the volume fraction of the reinforcing phase. The governing equations of motion for the rotating truncated composite conical shells are derived and solved numerically by means of the Generalized Differential Quadrature (GDQ) method combined with the third-order shear deformation theory (TSDT) in small deformations. The GDQ approach has recently emerged as a very promising numerical tool to solve complex problems without passing through any variational formulation, but solving directly the equations of motion in a strong form. In this paper, a parametric study based on the GDQ is systematically performed to exploit the effect of some geometry parameters, i.e. the length, the radius, the thickness and the semi-vertex angle of the cone, as well as the different distribution of CNTs along the thickness, on the frequency at different circumferential wave numbers and rotating speeds. A convergence study of the numerical results is also made in terms of deflection and stress distributions of the structure, which proves the efficiency of the GDQ approach, also for coarse mesh discretizations in the meridional direction.