Vibration Characteristics and Unstable Regions of a Functionally Graded GPL-Reinforced Aluminum-Based Truncated Conical Shell with 1:1 Internal Resonance

This paper provides a full-scale parametric study on the dynamic characteristics and unstable regions of a functionally graded graphene platelet-reinforced (FG-GPLR) aluminum-based truncated conical shell under 1:1 internal resonance condition. The modified Halpin–Tsai mechanical model is applied to predict the effective physical property parameters of the FG-GPLR aluminum-based truncated conical shell under different graphene distributions (GPL-U, GPL-O, and GPL-X). First, under the influence of temperature, based on the first-order shear deformation theory and von-Karman nonlinear strain–displacement relations, the motion equations of the simply supported FG-GPLR aluminum-based truncated conical shell are obtained using Hamilton’s principle and the Galerkin method. Second, by applying the multi-time scale perturbation analysis method, the coupled averaged equations in polar coordinates are derived. Subsequently, amplitude–frequency and force–amplitude response curves are plotted to study the effects of various parameters, including graphene distribution, graphene weight fraction, in-plane excitation amplitude, tuning parameter, structural dimensions of GPLs, temperature, damping coefficients, and phase angle, on the vibration characteristics. Finally, the unstable regions of the zero solution under different parameter variations are analyzed based on the Jacobian matrix. The results indicate that the GPL-X distribution is the optimal graphene distribution. The weight fraction of graphene is the primary factor influencing the vibration characteristics and unstable regions.