Nonlinear vibration response of higher-order shear deformable FG-CNTRC conical shells

In this work, the large-amplitude free and forced vibrations of functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shells are investigated based on the higher-order shear deformation theory. In order to obtain the governing equations, the metricized energy functional of the structure is presented based on the higher-order shear deformation theory (HSDT) and von-Karman geometric nonlinearity. Then, the variational differential quadrature (VDQ) method is adopted to present the discretized energy functional. The numerical time differential operators together with the arc-length continuation scheme are utilized to solve the governing equations and find the free and forced vibration responses. In order to evaluate the influences of reinforcement factors and geometrical parameters on the nonlinear vibration behavior, various numerical results are reported. The numerical results reveal that the increase of semi-vertex angle of the shell increases the nonlinear to linear frequency ratio.