Transient response of functionally graded carbon nanotubes reinforced composite conical shell with ring-stiffener under the action of impact loads

The mathematical model of transient response of functionally graded carbon nanotubes reinforced conical shell with ring-stiffener is derived. The deformation state of the conical shell is described by the Reddy higher-order shear deformation theory. The deformation of the isotropic ring-stiffener is described by the Euler-Bernoulli hypotheses. The Rayleigh-Ritz method is used to analyze the eigenmodes of the nanocomposite structure. Displacements projections and rotations of middle surface normal are the main unknowns of the problem. The mathematical model of the structure transient response is obtained as the linear dynamical system with respect to generalized coordinates. The assumed mode method is used to obtain this dynamical system. The influence of the type of carbon nanotube composite reinforcement on the amplitudes of the transient responses is analyzed. As follows from the numerical simulations, the top ring-stiffener significantly decreases the amplitudes of the transient response of the nanocomposite structure.