Analysis of Vibration Response in Graphene-Reinforced Aluminum-Based Truncated Conical Shells Under 1:2 Internal Resonance Conditions

Graphene-reinforced aluminum-based materials perfectly combine the excellent properties of graphene and aluminum, achieving superior lightweight structural characteristics. This study focuses on 1:2 internal resonance, analyzing the amplitude–frequency and force–amplitude responses of a graphene-platelet-reinforced aluminum-based truncated conical shell under multiple external excitations. Considering three different graphene distributions, an improved Halpin–Tsai mechanical model is used to predict the effective Young’s modulus of the GPL-enhanced aluminum-based truncated conical shell. Under temperature effects, based on the Reissner–Mindlin theory and von-Karman geometric nonlinear strain–displacement relationships, Hamilton’s principle and the Galerkin method are employed to derive the motion equations of the GPL-enhanced aluminum-based truncated conical shell. Through multiscale perturbation analysis, the averaged equations in polar coordinates are further derived. Based on the combined averaged equations, the amplitude–frequency and force–amplitude response curves of the system are plotted, investigating the influence of graphene distribution, graphene content, external excitation amplitude, tuning parameters, and graphene plate geometrical dimensions on its vibration characteristics. The analysis results indicate that graphene content is one of the primary factors affecting the vibration characteristics of graphene-reinforced aluminum-based truncated cones.