Nonlinear vibrations of carbon fiber double-curved sandwich shells with viscoelastic cores incorporating embedded carbon nanotubes

The present study investigates the free vibration and nonlinear chaotic vibration phenomena of a doubly-curved sandwich shell composed of carbon fiber reinforced polymer (CFRP) embedding carbon nanotube viscoelastic polymer cores (CNT). The present paper establishes a set of partial differential equations for motion under movable sandwich boundary conditions. The derivation of these equations utilizes the third-order Reddy theory, the von Karman relation, and Hamilton's principle. Through the integration and homogenization of the material along the thickness direction, equivalent tensile, bending, coupled, and higher-order stiffness matrices were obtained. The integration of the triangular Airy stress function with the Galerkin method facilitates the transformation of the system into a nonlinear ordinary differential equation with two degrees of freedom. The accuracy of the natural frequencies calculated by this model was verified by comparing them with those reported in the literature. The present study further investigates the free vibration characteristics of a three-phase composite material, whose surface carbon fibers and graphene plates (GPLs) synergistically reinforce. The analysis examines the influence of various parameters on the dimensionless natural frequency across four interlayer thickness configurations. The present study utilizes the fourth-order Runge-Kutta method under two distinct core thickness configurations to investigate the time-domain waveform, bifurcation curve, maximum Lyapunov exponent spectrum, and chaotic response curve. A comprehensive study examines the effects of uniformly distributed lateral loads and in-plane loads on the nonlinear dynamics of a CFRP-CNT doubly-curved sandwich spherical shell. The results indicate that, as the thickness proportion of the viscoelastic core layer decreases, the in-plane load amplitude required to suppress chaotic motion becomes smaller, and periodic motion occurs more frequently.