Nonlinear Vibration Response of Composite Conical Shells Reinforced with Carbon Nanotubes and Graphene Nanoplatelets Using a Stress Function Method

Abstract

This paper investigates the nonlinear vibrational behavior of nanocomposite conical shells reinforced with carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) within a polymer matrix. A hierarchical micromechanical model is first developed to predict the effective properties of the nanocomposite, considering critical microstructure-level structural phenomena. Initially, using the finite element method and a representative volume element (RVE), the effective properties of the polymer containing CNTs and GNPs are determined. To realistically simulate the nanocomposite's microstructure, CNTs and GNPs are dispersed randomly within the polymer matrix through a comprehensive algorithm. Applying a prescribed displacement to the RVE faces and calculating the resulting reaction forces allows for the extraction of the nanocomposite shell's effective properties. Furthermore, using Hamilton's principle and incorporating von Kármán nonlinear strains, the equations of motion are derived. Through the stress function approach and the Galerkin method, these equations are transformed into an ordinary differential equation. The study examines the effects of nanocomposite properties - such as the volume fractions of GNPs and CNTs, the presence or absence of the interphase region, the agglomeration of nanofillers within the RVE, CNT aspect ratio, and GNP thickness - on the vibration behavior of the conical shell for the first time. Results indicate that increasing the volume fraction of CNTs enhances the natural frequency of the shell, whereas accounting for nanofiller agglomeration reduces the strength and stiffness of the shell. © 2026 World Scientific Publishing Company.