Chaos and bifurcation analyses of functionally graded composite spherical shallow shells reinforced with graphene nanoplatelets

Functionally graded (FG) graphene nanoplatelets reinforced composite (FG-GPLRC) structures are expected to be greatly developed in engineering due to their excellent mechanical properties. The nonlinear dynamic behaviors such as chaos and bifurcation are particularly important. This article explores the nonlinear dynamics of FG-GPLRC shallow shells with three different GPL distribution patterns under the transverse and the in-plane excitation. The effective material properties of the composite material were calculated using an improved Halpin-Tsai model and the mixture rule. Using the Hamilton's principle and the high-order shear deformation theory (HSDT) to design a nonlinear mathematical model of simply supported spherical shallow shells. Numerical analysis shows that the weight fraction, the layer number, and the length-to-thickness ratio of GPL have significant effects on the mechanical behavior. These parameters have varying sensitivities to different GPL distribution patterns. The X-shaped distribution is more capable of withstanding larger external excitation compared to the U-shaped and O-shaped. The O-type distribution is more sensitive to the layer number. The mechanical behavior of the two modes also different after exceeding the critical value. This article focuses on providing effective theoretical guidance for practical engineering by simulating the mechanical behavior of structures under complex excitations.