Nonlinear vibration of multilayer shell-type structural elements with double curvature consisting of CNT patterned layers within different theories

In this article, the nonlinear vibration of moderately thick multilayer shell?type structural elements with double curvature consisting of carbon nanotube (CNT) patterned layers is investigated within different shell theories. The first order shear deformation theory has been generalized on the motion for moderately thick multilayer shell?type structural elements with double curvature consisting of CNT patterned layers for the first time. Then, by applying Galerkin and semi?inverse perturbation methods to motion equations, and the frequency? amplitude relationship is obtained. From these formulas, the expressions for nonlinear frequencies of multilayer spherical and hyperbolic?paraboloid shells, rectangular plate and cylindrical panels patterned by CNTs within shear deformation and classical shell theories are obtained in special cases. The reliability of obtained results is verified by comparison with other results reported in the literature. The effects of transverse shear strains, volume fraction, sequence and number of nanocomposite layers on nonlinear frequency are discussed in detail.