Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells

Abstract The influences of centrifugal and Coriolis forces on the free vibration behavior of rotating carbon nanotube reinforced composite (CNTRC) truncated conical shells are examined. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and are estimated through a micromechanical model. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells using Hamilton’s principle. The initial mechanical stresses are obtained by solving the dynamic equilibrium equations. The differential quadrature method (DQM) is adopted to discretize the equations of motion and the related boundary conditions. After demonstrating the convergence and accuracy of the presented approach, the effects of angular velocity, Coriolis acceleration, geometrical parameters, type of distribution and volume fractions of carbon nanotubes on the frequency parameters of the CNTRC truncated conical shells are studied. The results reveal that the influences of the type of carbon nanotube distribution and its volume fraction on the frequency parameters depend on the semi vertex angle and angular velocity of the shells and the frequency parameters of the shell with FG asymmetric carbon nanotube distribution can become greater than those of the case with FG symmetric distribution ones.