Large amplitude vibration of FG-CNTRC laminated cylindrical shells with negative Poisson’s ratio

This paper presents an investigation on the nonlinear flexural vibrations of carbon nanotube-reinforced composite (CNTRC) laminated cylindrical shells with negative Poisson’s ratios in thermal environments. The material properties of the CNTRCs are temperature-dependent and the functionally graded (FG) in a piece-wise pattern in the thickness direction of the shell. An extended Voigt (rule of mixture) model is employed to estimate the CNTRC material properties. The motion equations for the nonlinear flexural vibration of FG-CNTRC laminated cylindrical shells are based on the Reddy’s third order shear deformation theory and the von Kármán-type kinematic nonlinearity, and the effects of thermal environmental conditions are included. The nonlinear vibration solutions for the FG-CNTRC laminated cylindrical shells can be obtained by applying a singular perturbation technique along with a two-step perturbation approach. The effects of material property gradient, the temperature variation, shell geometric parameter, stacking sequence as well as the end conditions on the vibration characteristics of CNTRC laminated cylindrical shells are discussed in detail through a parametric study. The results show that negative Poisson’s ratio has a significant effect on the linear and nonlinear vibration characteristics of CNTRC laminated cylindrical shells. •Both piece-wise FG configurations and NPRs are considered.•A multi-scale approach is proposed for nonlinear vibration of auxetic CNTRC shells.•NPR has a significant effect on the nonlinear vibration behavior of FG-CNTRC shells.