Geometrically nonlinear higher-order shear deformable model of TiO2/GNP/polymer nanocomposite rectangular plates: A numerical study on mechanical properties and nonlinear primary resonance features

Nonlinear primary resonance behavior of titanium dioxide (TiO₂)/graphene nanoplatelet (GNP)/polymer nanocomposite rectangular plates using a geometrically nonlinear higher-order shear deformable plate model is investigated. The material properties of the hybrid nanocomposite, consisting of a polymer matrix reinforced with TiO₂ nanoparticles and GNPs are determined through the finite element-based micromechanical modeling. The representative volume elements (RVEs) account for nanofiller geometry, dispersion patterns, and interphase effects to accurately simulate the mechanical properties of the nanocomposite. The nonlinear governing equations of motion are derived using Reddy's third-order shear deformation theory and von Kármán nonlinearity and are discretized via the generalized differential quadrature (GDQ) method. The equations are solved using a multistage numerical procedure combining the Galerkin approach, time periodic discretization (TPD) scheme, and pseudo-arc length continuation technique to obtain nonlinear frequency-response curves under various boundary conditions. The results highlight the pronounced contribution of GNP reinforcement, which significantly enhances the stiffness and nonlinear hardening behavior of the plates, as evidenced by increased linear and nonlinear frequencies and reduced vibration amplitudes.