Nonlinear damped vibrations of three-phase CNT-FRC circular cylindrical shell

This study presents a semi-analytical solution of nonlinear vibrations of circular cylindrical shells made of carbon nanotube (CNT) fiber-reinforced composite (CNT-FRC). Vibrations are produced by a radial harmonic force and viscous structural damping is considered. The effective properties of a lamina of the CNT-FRC shell are evaluated in two steps. The elastic properties of randomly distributed CNTs in a polymeric matrix (i.e., hybrid matrix) are computed by the Eshelby-Mori-Tanaka/Voigt scheme to consider the CNTs agglomeration effect in the hybrid matrix. Then, the resulting hybrid matrix is reinforced with aligned fibers in order to prepare the lamina of the CNT-FRC shell; its effective properties are estimated by the Halpin Tsai homogenization approach. The CNT-FRC shell is modelled incorporating the von Kármán geometric nonlinearity and first-order shear deformation theory (FSDT). The nonlinear governing partial differential equations (PDEs) of the CNT-FRC shells are derived by the Hamilton's principle. These PDEs are discretized into ordinary differential equations (ODEs) by using the Galerkin's method. The ODEs are solved by incremental harmonic balance method (IHB) in conjunction with the arclength continuation method to obtain the frequency-amplitude response of the shell. The effect of different types of CNT agglomeration models, CNT mass fraction, agglomeration parameters and stacking sequence of laminates on the frequency-amplitude curves corresponding to forced and free nonlinear vibrations of the CNT-FRC shell are studied in detail.