Nonlinear vibration analysis of CNT-reinforced functionally graded composite cylindrical shells resting on elastic foundations

Nonlinear vibration analysis of carbon-nanotube reinforced functionally graded composite (FG-CNTRC) cylindrical shells resting on elastic foundations is carried out. Four carbon nanotube distributions, namely UD, FGV, FGΛ and FGX, are considered and the elastic foundation is described using the Pasternak model. According to the first-order shear deformation shell theory, the nonlinear governing equations of FG-CNTRC cylindrical shells are derived from Lagrange equations. The forced nonlinear vibrations of FG-CNTRC cylindrical shells with/without surrounding elastic media are then investigated using the harmonic balance method combined with the arc length continuation technique, and chaotic vibrations due to the 1:1 internal resonance are further studied through direct integration. Finally, the effects of the distribution patterns and the stiffness of elastic foundations on the nonlinear behaviors of FG-CNTRC cylindrical shells are presented in detail. •Nonlinear vibration of carbon-nanotube reinforced functionally graded composite (FG-CNTRC) cylindrical shells is carried out.•Effects of the CNT distribution patterns on the nonlinear behaviors of FG-CNTRC cylindrical shells are presented.•Effects of the stiffness of elastic foundations on the nonlinear behaviors of FG-CNTRC cylindrical shells are investigated.