Effects of non-uniformity in thickness and volume fraction of agglomerated CNTs on the dynamics of a spinning CNT-reinforced nanocomposite truncated conical shell

In the presented work, the free vibration analysis of a rotating truncated conical shell whose thickness varies in the meridional direction is examined. The material that the shell is made of is a polymeric matrix (epoxy) enriched with carbon nanotubes (CNTs) whose volume fraction varies in the meridional direction. CNTs agglomeration is considered and the density and elastic constants of such a two-phase nanocomposite are calculated sequentially based on the Eshelby–Mori–Tanaka approach alongside the rule of mixture. The conical shell is modeled using the first-order shear deformation theory (FSDT) including the relative acceleration, Coriolis acceleration, and centrifugal acceleration along with the initial hoop tension, and the governing equations are obtained utilizing Hamilton’s principle. The solution of governing equations is performed via the combination of an analytical solution in the circumferential direction and a numerical one in the meridional direction via the differential quadrature method (DQM). The impacts of several parameters on the forward and backward natural frequencies of such a rotating shell are studied such as chirality, mass fraction and dispersion pattern of the CNTs, thickness variation parameters, and boundary conditions. It is observed that higher natural frequencies and critical rotational speeds can be achieved for CNT-reinforced conical shells when the volume fraction of the CNTs and the thickness of the shell increase from its small radius to the large one.