Geometrically nonlinear free oscillations of ternary SGF/CNT nanocomposite annular sector plates via a unified micromechanics–time-periodic discretization approach

Abstract

In this study, with the aid of a unified micromechanics–time-periodic mathematical model, the geometrically nonlinear free oscillation characteristics of higher-order shear deformable ternary short glass fiber (SGF)/carbon nanotube (CNT) nanocomposite annular sector plates are investigated considering the influences of different material and structural parameters. The effective mechanical properties of the nanocomposite are derived using a finite element-based micromechanical modeling, accounting for the contributions of SGFs and CNTs. The nonlinear governing equations are formulated by utilizing von Kármán nonlinearity relations and solved using a multiphase numerical solving strategy that includes the Galerkin scheme, time-periodic discretization (TPD) approach, pseudo-arc-length continuation method, and modified Newton–Raphson technique. The nonlinear frequency responses are obtained, and the effects of CNT and SGF volume fractions, aspect ratios, dispersion patterns, interphase effects, and CNT morphology are comprehensively analyzed. The results indicate that increasing CNT and SGF volume fractions significantly enhances the nonlinear frequencies of the nanocomposite structure, with higher aspect ratios leading to further improvements. It is also concluded that the alignment of both fillers provides the highest dynamic performance for SGF/CNT nanocomposite annular sector plates. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.