Spectro-geometric solutions for random vibration of functionally graded graphene platelet reinforced conical shells

Abstract

This study delved into the random vibration characteristics of a conical shell constructed from a functionally graded graphene platelet-reinforced composite (FG-GPLRC) under the influence of basic acceleration excitation. The investigation employed a synthesis of two methodologies: the spectro-geometric method (SGM) and the pseudo-excitation method (PEM). Commencing with the application of the Halpin–Tsai micromechanics approach and the law of mixtures, the effective material characteristics of the FG-GPLRC structure were determined. Subsequently, the displacement field vector for the conical shell structure was established with SGM. By employing the framework of the first-order shear deformation theory (FSDT), the energy function of the FG-GPLRC conical shell was derived, with external random excitation energy being incorporated with PEM. To construct a dynamic model for the conical shell structure, the Rayleigh-Ritz method was applied, subjecting the energy function to variational extremization. This approach yielded a comprehensive dynamic representation. The validity of the proposed model was substantiated through comparison with existing literature and finite element method results. Ultimately, this study explored the influence of graphene material properties and geometric parameters of the conical shell on the random vibration characteristics of the FG-GPLRC conical shell.